Cadaei

05-05-2014, 01:42 AM

Technical, conceptual, curiosities you've had, try to make me look stupid, whatever. Finals in two weeks and this is a cute way to practice.

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View Full Version : ITT: I Study for My Final by Answering your Quantum Mechanics Questions

Cadaei

05-05-2014, 01:42 AM

Technical, conceptual, curiosities you've had, try to make me look stupid, whatever. Finals in two weeks and this is a cute way to practice.

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joshewwah

05-05-2014, 01:48 AM

What is Quantum physics?

Cadaei

05-05-2014, 01:55 AM

What is Quantum physics?

The physics we use to describe things that are very small. The name "quantum" comes from the fact that many things normally described as continuous can be described with quanta at this scale (e.g, the photon for light).

The physics we use to describe things that are very small. The name "quantum" comes from the fact that many things normally described as continuous can be described with quanta at this scale (e.g, the photon for light).

MiscMathematician

05-05-2014, 01:57 AM

How does one instruct a quantum "CPU" to perform tasks?

Cadaei

05-05-2014, 01:58 AM

How does one instruct a quantum "CPU" to perform tasks?

perform "operations" on q-bits, which are a special kind of entangled wavestate. the EPR state is the simplest

perform "operations" on q-bits, which are a special kind of entangled wavestate. the EPR state is the simplest

ThePizzaMan

05-05-2014, 03:52 AM

What were the fundamental results of Schrödinger's cat experiment and how/what did it contribute to the quantum theory?

canconfirm

05-05-2014, 05:58 AM

if you put a potato next to OP what's the difference?

Psychromatik

05-05-2014, 06:22 AM

Please elaborate on the cause of the magnetic field in a permanent magnet and if it is related to an electron's 'spin'. If so, how does the magnet somehow maintain this perpetual momentum to propagate the field?

Cadaei

05-05-2014, 06:04 PM

What were the fundamental results of Schrödinger's cat experiment and how/what did it contribute to the quantum theory?

Schrodinger’s cat is a thought experiment meant to make the Copenhagen interpretation of quantum mechanics look absurd.

Some background: In QM, particles are often considered to be in a superposition of multiple states. For example the wave function describing the spin state of an electron is a linear combination of the spin-up and spin-down states. Until a measurement is made to collapse the wavefunction to one of these states, the interpretation is that the particle is smeared out in both. Spin is just an example - this is how all quantum states are described.

Schrodinger thought this interpretation was absurd. He created the following thought experiment:

Put a cat in a box with a canister of poison gas. Also put in this box a single particle of a radioactive source such that the probability to decay in some time period is equally as likely as it not decaying. Finally attach a Geiger counter to the poison, and rig it so that if the Geiger counter measures a decay it releases the poison, and if it doesn’t measure it, it doesn’t release the poison. Now seal the box so that no outside observer can see it.

After sufficient time has passed so that the probability of decay and not decay is equally likely, Schrodinger thinks the interpretation must be that the cat is smeared across two states, death and not death, until the box is opened, constituting a “measurement” that collapses the state into one of the two eigenstates.

The Copenhagen interpretation is saved, however, by taking the Geiger counter to be the measurement device. This is important because it makes clear what constitutes a measurement that is capable of collapsing a wavefunction, and also that such a measurement need not be done by a conscious observer.

Please elaborate on the cause of the magnetic field in a permanent magnet and if it is related to an electron's 'spin'. If so, how does the magnet somehow maintain this perpetual momentum to propagate the field?

Yes you guessed correctly. Macroscopic magnetism as seen in a permanent magnet is related to the spin of the electron.

First, what is spin? Spin is an angular momentum, and it is an *intrinsic* property just like charge, mass, etc. All electrons have spin one-half and the magnitude of this spin cannot be changed. The direction of the spin is either “up” or “down” when measured and cannot be anything in between. The name “spin” used to have physical meaning when it was interpreted as the electron spinning on its axis, but it doesn’t anymore because the electron is no longer interpreted as just a particle but also as a wave. In modern times we just keep the name “spin” for historical reasons.

Magnetism is described by a quantity called the magnetic dipole moment, and an electron has one of these dipole moments.

Why does it have such a thing? You guessed it. Spin. The magnetic dipole moment for an electron just turns out to be proportional to its spin by some uninteresting constants. This dipole is so extremely tiny that it has yet to be measured in a laboratory. However, if we align all of the spins in the same direction, we can see this magnetic effect at macroscopic levels because the dipole moment is a vector quantity (e.g., the dipole moments just add if they are pointing in the same direction).

Thus you can make permanent magnet from a “ferromagnetic material”, which is a fancy way to say “a material whose structure is rigid enough that we can align all of these tiny little spins relatively permanently, so we can see all their tiny little effects add up on human scales.”

Schrodinger’s cat is a thought experiment meant to make the Copenhagen interpretation of quantum mechanics look absurd.

Some background: In QM, particles are often considered to be in a superposition of multiple states. For example the wave function describing the spin state of an electron is a linear combination of the spin-up and spin-down states. Until a measurement is made to collapse the wavefunction to one of these states, the interpretation is that the particle is smeared out in both. Spin is just an example - this is how all quantum states are described.

Schrodinger thought this interpretation was absurd. He created the following thought experiment:

Put a cat in a box with a canister of poison gas. Also put in this box a single particle of a radioactive source such that the probability to decay in some time period is equally as likely as it not decaying. Finally attach a Geiger counter to the poison, and rig it so that if the Geiger counter measures a decay it releases the poison, and if it doesn’t measure it, it doesn’t release the poison. Now seal the box so that no outside observer can see it.

After sufficient time has passed so that the probability of decay and not decay is equally likely, Schrodinger thinks the interpretation must be that the cat is smeared across two states, death and not death, until the box is opened, constituting a “measurement” that collapses the state into one of the two eigenstates.

The Copenhagen interpretation is saved, however, by taking the Geiger counter to be the measurement device. This is important because it makes clear what constitutes a measurement that is capable of collapsing a wavefunction, and also that such a measurement need not be done by a conscious observer.

Please elaborate on the cause of the magnetic field in a permanent magnet and if it is related to an electron's 'spin'. If so, how does the magnet somehow maintain this perpetual momentum to propagate the field?

Yes you guessed correctly. Macroscopic magnetism as seen in a permanent magnet is related to the spin of the electron.

First, what is spin? Spin is an angular momentum, and it is an *intrinsic* property just like charge, mass, etc. All electrons have spin one-half and the magnitude of this spin cannot be changed. The direction of the spin is either “up” or “down” when measured and cannot be anything in between. The name “spin” used to have physical meaning when it was interpreted as the electron spinning on its axis, but it doesn’t anymore because the electron is no longer interpreted as just a particle but also as a wave. In modern times we just keep the name “spin” for historical reasons.

Magnetism is described by a quantity called the magnetic dipole moment, and an electron has one of these dipole moments.

Why does it have such a thing? You guessed it. Spin. The magnetic dipole moment for an electron just turns out to be proportional to its spin by some uninteresting constants. This dipole is so extremely tiny that it has yet to be measured in a laboratory. However, if we align all of the spins in the same direction, we can see this magnetic effect at macroscopic levels because the dipole moment is a vector quantity (e.g., the dipole moments just add if they are pointing in the same direction).

Thus you can make permanent magnet from a “ferromagnetic material”, which is a fancy way to say “a material whose structure is rigid enough that we can align all of these tiny little spins relatively permanently, so we can see all their tiny little effects add up on human scales.”

Purplekoolaid

05-05-2014, 06:20 PM

how do you know whether to use trig functions or exponentials when solving shrodinger's time-independent diff eq?

Comboking

05-05-2014, 07:03 PM

if you only saw the imprint of my dink through my sweaty sweat pants at the gym while i was incline pressing at a 45degree angle, what size is the gap of my anus

USAviator

05-05-2014, 07:12 PM

5 inches due to the big black dingus in your dungus

IsLifeRealLife

05-05-2014, 07:16 PM

Prove that for any compact single gauge group G, quantum Yang-Mills theory of R^4 exists and has a mass gap > 0

Supadude

05-05-2014, 07:35 PM

What happens when an unstoppable force meets an unmovable object?

Cadaei

05-05-2014, 07:46 PM

how do you know whether to use trig functions or exponentials when solving shrodinger's time-independent diff eq?

They both will always work because of Euler's formula (assuming you're talking about a potential for which this form is the solution). You can sometimes make it just one sine or cosine though. For example square well wavefunctions that run from 0 to a can be represented by a single sine to get both even and odd solutions.

So the answer is whenever you suspect the form of one representation will make the solution look prettier or easier to work with. Generally for plane wave forms you use exponentials, and differentiation and integration is usually way easier with exponential form if you're working on them.

They both will always work because of Euler's formula (assuming you're talking about a potential for which this form is the solution). You can sometimes make it just one sine or cosine though. For example square well wavefunctions that run from 0 to a can be represented by a single sine to get both even and odd solutions.

So the answer is whenever you suspect the form of one representation will make the solution look prettier or easier to work with. Generally for plane wave forms you use exponentials, and differentiation and integration is usually way easier with exponential form if you're working on them.

Cadaei

05-05-2014, 07:48 PM

Prove that for any compact single gauge group G, quantum Yang-Mills theory of R^4 exists and has a mass gap > 0

Cute. To aware y'all, this is an unsolved problem, the reward for which is a million dollars.

Cute. To aware y'all, this is an unsolved problem, the reward for which is a million dollars.

Odin21

05-05-2014, 09:38 PM

Cute. To aware y'all, this is an unsolved problem, the reward for which is a million dollars.

what would the answer to this question be used for?

also how many atoms comprise my weiner? its about 7.25 inches long

what would the answer to this question be used for?

also how many atoms comprise my weiner? its about 7.25 inches long

Cadaei

05-06-2014, 09:46 PM

what would the answer to this question be used for?

First let's try to get a notion for a what a gauge is. Modern physics is based on notions of fields, such as gravitational fields or electromagnetic fields. Fields themselves are defined in terms of derivatives of potentials. Thus, since there is a whole family of functions g(x) = f(x) + c such that g'(x) = f'(x) (in other words, because the arbitrary constant goes away with the derivative), potentials g and f both describe the same field. There are infinite such g that will do this. Do you remember from basic E&M that we can choose the zero of the coulomb potential to be wherever we want it to be, because all we care about is changes in potential? Well, guess what? That's a gauge freedom.

A gauge transformation is a change made to a potential that gives rise to the same field. For example, using our coulomb example, changing the zero from one point to another constitutes a gauge transformation.

There are certain theories that we like to call "gauge theories." These are theories for which the Lagrangian is invariant under a gauge transformation. The Lagrangian is just a fancy way to say "the equation that represents the dynamics of the system."

So where does this come into play? Well the Yang-Mills theory is one of these gauge theories. It's provides the basis for our theoretical understanding of the electroweak interactions as well as the strong force in the standard model. The problem is that this has not been rigorously proven or defined for spacetime (R^4) .

also how many atoms comprise my weiner? its about 7.25 inches long

I'm guessing your weiner is about the width of a pencil, ~5mm, so it's volume is (7.25*2.54*pi*(.5)^2/4) = 3.62 cm^3.

Human tissue is mostly water, so since this question is absurd anyway, let's just say assuming that its entirely water will give an answer to within an order of magnitude.

[ 3.62 cm^3 * (1g/cm^3) ] / (18.0 g/mol {for H2O} ) *6.022 *10^23 (mol^-1) * (3 atoms/1 water molecule) = 3.63 * 10 ^23

-> ~ 10^23 atoms in your dink

First let's try to get a notion for a what a gauge is. Modern physics is based on notions of fields, such as gravitational fields or electromagnetic fields. Fields themselves are defined in terms of derivatives of potentials. Thus, since there is a whole family of functions g(x) = f(x) + c such that g'(x) = f'(x) (in other words, because the arbitrary constant goes away with the derivative), potentials g and f both describe the same field. There are infinite such g that will do this. Do you remember from basic E&M that we can choose the zero of the coulomb potential to be wherever we want it to be, because all we care about is changes in potential? Well, guess what? That's a gauge freedom.

A gauge transformation is a change made to a potential that gives rise to the same field. For example, using our coulomb example, changing the zero from one point to another constitutes a gauge transformation.

There are certain theories that we like to call "gauge theories." These are theories for which the Lagrangian is invariant under a gauge transformation. The Lagrangian is just a fancy way to say "the equation that represents the dynamics of the system."

So where does this come into play? Well the Yang-Mills theory is one of these gauge theories. It's provides the basis for our theoretical understanding of the electroweak interactions as well as the strong force in the standard model. The problem is that this has not been rigorously proven or defined for spacetime (R^4) .

also how many atoms comprise my weiner? its about 7.25 inches long

I'm guessing your weiner is about the width of a pencil, ~5mm, so it's volume is (7.25*2.54*pi*(.5)^2/4) = 3.62 cm^3.

Human tissue is mostly water, so since this question is absurd anyway, let's just say assuming that its entirely water will give an answer to within an order of magnitude.

[ 3.62 cm^3 * (1g/cm^3) ] / (18.0 g/mol {for H2O} ) *6.022 *10^23 (mol^-1) * (3 atoms/1 water molecule) = 3.63 * 10 ^23

-> ~ 10^23 atoms in your dink

Chunkithunder

05-06-2014, 09:55 PM

Does hybridization of s, p, and d orbitals of atoms count as quantum mechanics? If so, please explain them to me srs, just had a test on it in my chem class and did terrible on it

Cadaei

05-06-2014, 10:05 PM

Does hybridization of s, p, and d orbitals of atoms count as quantum mechanics? If so, please explain them to me srs, just had a test on it in my chem class and did terrible on it

It does count but I'm afraid you don't deal with it much in physics. It is in fact derived from approximations to the exact solution of Schrodinger equations, but in practice this is not how its taught in chem (I had to take that stupid class, too. I feel your pain). They basically just teach you to memorize it, which I can't really help you with.

But I can help you to picture what is going on. The electron clouds are described by wave functions, and when you get atoms, these wavefunctions must sum. The magnitude squared of the sums come out to be the shapes they make you memorize. Hope that helps.

It does count but I'm afraid you don't deal with it much in physics. It is in fact derived from approximations to the exact solution of Schrodinger equations, but in practice this is not how its taught in chem (I had to take that stupid class, too. I feel your pain). They basically just teach you to memorize it, which I can't really help you with.

But I can help you to picture what is going on. The electron clouds are described by wave functions, and when you get atoms, these wavefunctions must sum. The magnitude squared of the sums come out to be the shapes they make you memorize. Hope that helps.

BrollicWraith

05-06-2014, 11:14 PM

Will our solar system ever be sucked into the supermassive black hole at the center of our galaxy??

InsaneLuis

05-06-2014, 11:33 PM

Dude, I don't understand a single word of anything you are typing, but I seriously feel smart pronouncing and reading your posts. Thanks brah, and sorry for not contributing I just had to say it.

Cadaei

05-06-2014, 11:38 PM

Will our solar system ever be sucked into the supermassive black hole at the center of our galaxy??

Currently, we are orbiting that SMBH. And something being a blackhole doesn't actually change any orbital characteristics.

If our sun were to instantly become a blackhole right now (it can't - not massive enough) with the same mass, we wouldn't notice, except that 8 minutes after it happened it'd be very dark and we'd freeze to death quickly. But the earth would continue to orbit normally.

For the earth to end up in the black hole, something would have to drastically perturb our orbit and send us in that general direction.

However, in a big freeze scenario (the generally accepted fate of the universe), black holes will eventually come to be the dominant form of "matter" in the universe. However blackhole lifetimes are not infinite - blackholes evaporate via hawking radiation. The time for this to happen to *all* of the black holes in the universe is something like 10^44 years iirc, where everything has decayed into photons traveling through an empty void for all eternity.

Currently, we are orbiting that SMBH. And something being a blackhole doesn't actually change any orbital characteristics.

If our sun were to instantly become a blackhole right now (it can't - not massive enough) with the same mass, we wouldn't notice, except that 8 minutes after it happened it'd be very dark and we'd freeze to death quickly. But the earth would continue to orbit normally.

For the earth to end up in the black hole, something would have to drastically perturb our orbit and send us in that general direction.

However, in a big freeze scenario (the generally accepted fate of the universe), black holes will eventually come to be the dominant form of "matter" in the universe. However blackhole lifetimes are not infinite - blackholes evaporate via hawking radiation. The time for this to happen to *all* of the black holes in the universe is something like 10^44 years iirc, where everything has decayed into photons traveling through an empty void for all eternity.

Cadaei

05-06-2014, 11:40 PM

Dude, I don't understand a single word of anything you are typing, but I seriously feel smart pronouncing and reading your posts. Thanks brah, and sorry for not contributing I just had to say it.

<3 thanks brah

<3 thanks brah