Quantum mechanics describes the microscopic properties of nature in a regime where classical mechanics no longer applies. It explains phenomena such as the wave-particle duality, quantization of energy and the uncertainty principle and is generally used in single body systems. Use the quantum-field-...

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2answers
909 views

Normalization of the path integral

When one defines the path integral propagator, there is the need to normalize the propagator (since it would give you a probability density). There are two formulas which are used. 1) Original (v1+v2)...
3
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1answer
127 views

A change of sign in the electron-hole second quantization form

It is common to see people do a change of sign in the so called electron-hole representation, namely, $$ b^{\dagger}_{-k}=a_{v,k} $$ similar argument also seen in 1992 mattuck's book "guide to ...
3
votes
1answer
489 views

Minus Sign in Feynman Diagram

I've been reading these notes and I can't figure out the why on P.120, it is said that The fermionic statistics mean that the first diagram has an extra minus sign relative to the ψψ scattering ...
5
votes
1answer
458 views

Quantum tunneling effect in a potential of the kind $V(x)=A\frac{x^2}{1+x^4}$

Given a potential: $$V(x)=A\frac{x^2}{1+x^4}$$ with $A\gt 1$ and a quantum particle inside the well around the point $x=0$. I'm stuck on the calculation of the transmission and reflection coefficients ...
3
votes
1answer
673 views

Hubbard-Stratonovich transformation and mean-field approximation

For an interacting quantum system, Hubbard-Stratonovich transformation and mean-field field approximation are methods often used to decouple interaction terms in the Hamiltonian. In the first method, ...
4
votes
1answer
167 views

Entropy inequality

Assume that you have two bipartite systems $\rho_1^{AB},\rho_2^{AB}$ then I would like to prove the following: $$S(\frac{1}{2}( \rho_1^{AB}+I^A\otimes\rho_2^B))+S(\frac{1}{2}(\rho_2^{AB}+I^A\otimes\...
6
votes
1answer
2k views

How to tell theoretically whether an electron behaves as wave or particle

I have seen many questions on SE on the dual nature of electrons behaving in certain circumstances as particles and as waves in some other circumstance. There is one thing I couldn't get a clear ...
0
votes
2answers
111 views

Probability amplitude in basic quantum mechanics

I came across this proportionality statement in my quantum mechanics notebook: $\psi(x,t)$ is proportional to $$ \begin{align} \cos(kx - wt) &= \exp(i(kx-wt)) + \exp(-i(kx-wt)) \\ &= \exp (...
6
votes
1answer
119 views

Does gravity limit the number of bosons that can occupy the same single-particle state?

QFT says that an unlimited number of bosons can occupy the same "state" (what I mean by that is that the whole system's wavefunction is composed of a product of many identical wavefunctions). However,...
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0answers
265 views

A basic question about Heisenberg State Kets (in particular the simple harmonic oscillator)

I know base kets in the Heisenberg picture are $U^\dagger |{a}\rangle$ but if the base kets are the base of the hamiltonian, and the hamiltonian is independent of time, are all of the base kets ...
0
votes
1answer
494 views

Elastic collision of photon [closed]

Consider an elastic collision of a photon with 100 eV energy hitting a mirror. How much momentum is exchanged in the collision? Also, can one model the reflection of an elastically colliding photon ...
1
vote
3answers
5k views

Average Energy of the Quantum Harmonic Oscillator

In Griffiths, the average potential energy for the quantum harmonic oscillator is given as $$\langle V\rangle~=~\frac{1}{2}\hbar \omega(n+\frac{1}{2}).$$ Is the potential energy of the quantum ...
6
votes
1answer
481 views

Why does burning things make them black?

It's not clear to me how burning process can transform a material which was previously capable both of absorbing and emitting photon to one which can only absorb them. I would like to hear an educated ...
12
votes
3answers
2k views

How can we interpret polarization and frequency when we are dealing with one single photon?

If polarization is interpreted as a pattern/direction of the electric-field in an electromagnetic wave and the frequency as the frequency of oscillation, how can we interpret polarization and ...
-2
votes
2answers
561 views

Quantum entanglement? And quantum double slit

Does quantum entanglement consist only of 2 matter that are connected by each other? And what is the connection between the observer and the matter that is being fired? I'm not a physicist though ...
2
votes
1answer
121 views

What are the current obstacles to experimentally testing quantum pseudo telepathy?

Quantum pseudo-telepathy refers to how, in some specific coordination games, isolated players can do better when they have pre-shared some entangled qubits. I understand how it works in theory and ...
0
votes
1answer
2k views

Expectation value of total energy for the quantum harmonic oscillator [closed]

A particles unnormalized wavefunction is given as $$\psi(x)=2\psi_1+\psi_2+2\psi_3.$$ How can I find $\langle E\rangle $ without calculating $\langle T\rangle$ or $\langle V\rangle $ ...
2
votes
1answer
382 views

Open problem? Square of the wave function $\Psi(x)_{x_o} = \delta(x-x_0)$ of a particle localized at a point $x_0$?

Does anybody know the status of the problem to define the wave function (non-relativistic Quantum Mechanics) of a particle localized at a definite point? Landau-Lifshitz says in chapter 1 that this ...
0
votes
1answer
317 views

Find the possible energies and corresponding wavefunctions of the Hamiltonian [closed]

The Hamiltonian of an electron stuck within a tunnel in a dialectic cube is found to be $$H=\frac{p^2}{2m}+\frac{1}{2}Kx^2-\frac{e\Phi_0}{a}x$$ Find the possible energies and corresponding ...
0
votes
2answers
1k views

Occupation Number Representation in Second Quantization Formalism — What do the entries mean?

I'm reading about the second quantization formalism. I can see the advantages of using number states to represent multiparticle states. Here's my question: Let's say we're given a single-particle ...
2
votes
2answers
186 views

Measuring the spin of a particle from a singlet state

Imagine that I have a singlet state: $|s\rangle = {1 \over \sqrt2}(| \uparrow_1\downarrow_2 \rangle - |\downarrow_1\uparrow_2\rangle)$ I want to measure the spin along the z axis of the first ...
1
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0answers
162 views

Commutator problem

I am trying to calculate the following commutator $$[\mathcal{H}_0(r',t'),\psi(r,t)]_-$$ where $\mathcal{H}_0 = (\frac{1}{2m}\nabla^2 + e\mathbf{A}(r',t'))^2 + e\phi(r',t') - \mu$, and $\mu$ is the ...
3
votes
2answers
228 views

Workaround to fermion sign problem?

My (rather incomplete) understanding of the NP-hard fermion/numerical sign problem is that it occurs when attempting to converge on a wavefunction for many-body fermion systems (for example, a small ...
1
vote
3answers
146 views

Schrödinger Equation: Eigenmomentum?

I'm confused by my books treatment of the Schrödinger equation. In steado f listing my questions at the end of my post, I'll add them as questions in parentheses after the line in question. For a ...
0
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0answers
218 views

Hydrogen atom in partial differential equations, show it is is independent of time. [closed]

For the hydrogen atom, if $\int|u|^2\ \mbox{d}x=1$ show that the same is true at all later times. Hint: Differentiate the integral with respect to t, taking care about the solution being complex ...
5
votes
1answer
1k views

Reduced mass in quantum physics (Hydrogen Atom)

I've gone through an intermediate classical mechanics course, and in solving the two-body problem, we reduce it to a one-body between a larger stationary mass, and a smaller reduced mass. Most ...
1
vote
1answer
171 views

Meaning of $C$ in wavefunction equation ($\Psi_{MO} = C_1\phi_A(1s) + C_2\phi_B(1s)$, where $C_1=\pm C_2$)

I've just cracked open a biophysics textbook and it's all fine up until the introduction of the letter C in a wavefunction equation, and declaring C1= ±C2 I've had lectures on eigenfunctions etc. ...
2
votes
1answer
93 views

Why does bringing N 1-orbital atoms together yield N levels?

A common example of this is that when bringing N hydrogen atoms together into a ring. Far apart, assume each electron exists in the 1s state. As we bring them together, instead of each electron ...
2
votes
1answer
219 views

Almost identical fermions fighting for the same state

In quantum 101, we all learned that identical particles behave strangely, even in the absence of interactions: no two fermions can be in the same state, but bosons love to be in the same state. But ...
9
votes
1answer
408 views

Is a QFT in a classical curved spacetime background a self-consistent theory?

EDIT: Better rewording by Chris White: Is it possible to have a theory that treats both GR and QFT (e.g. QFT on a curved spacetime dynamically influenced by the standard QFT fields)? Is such a theory ...
1
vote
2answers
139 views

Why don't charges move transverse to an EM wave?

Image we have an ultra-high intensity, ultra low frequency laser, with wattage on the order of terawatts and a wavelength on the order of a lightsecond. We rotate it that the electric field component ...
2
votes
1answer
9k views

Proof that the momentum operator is Hermitian

I am trying to prove that the momentum $p_x$ operator is Hermitian, my approach is the following $$<p_x>~=~\int \Psi^*(\vec{r},t)[-ih\frac{\partial}{\partial x}]\Psi(\vec{r},t)\, d^3r.$$ I try ...
2
votes
3answers
166 views

Non-normalizable QM bound state in 4 spatial dimensions?

Edit 26/Sept/13: Fixed Typo in potential I'm solving the following (seemingly simple) quantum-mechanical problem in four spatial dimensions. In natural units ($\hbar^2/2m=1$), the Schrödinger ...
2
votes
2answers
293 views

Angular momentum of quantum system

Problem: A physical system is in the common eigenstate of $\hat{L^2}$ and $\hat{L_z}$. Calculate the following quantities: $\langle L_x\rangle,\langle L_y\rangle,\langle L_z\rangle,\langle L_x L_y + ...
2
votes
2answers
3k views

Angular Momentum commuting with Hamiltonian

I've been given an assignment where I have to prove that the angular momentum operators $L_j = \varepsilon_{jkl}q_{k}p_{l}$ commute with the Hamiltonian, given as $H = \frac{p^2}{2m} + V(r)$. Now, I ...
1
vote
1answer
402 views

Wavefunction's inner product

When two wavefunctions are orthogonal we can write that $$\langle\Psi_n|\Psi_m\rangle=\delta_{mn}$$ This means that $$\langle\Psi_1|\Psi_2\rangle=\langle\Psi_2|\Psi_1\rangle=0$$ But if the two ...
1
vote
1answer
523 views

How to determine the amount of light energy (photons) being released from an incandescent light bulb?

I have got this all down pat: 1.Collision with a moving particle excites an atom. 2.This causes an electron to jump to a higher energy level. 3.The electron falls back to its original energy level, ...
0
votes
2answers
224 views

More Heisenberg Uncertainty Principle (HUP) Clarification

If you look at the commutation relation of the position and momentum operators (in 1D position space), you get: $$[\hat{x}, \hat{p}_x] = [x,-i \hbar \frac{\partial}{\partial x}] = i \hbar$$ All this ...
26
votes
2answers
6k views

What is a phonon?

I am trying to understand intuitively what a phonon is, but for the moment I find it quite difficult (having a limited background in quantum mechanics, an undergraduate course in non-relativistic QM). ...
3
votes
3answers
238 views

Translation operator to higher order

IN QM, the space translation operator, or generator of Translations is set to be Ie-ie/h_bar*P up to order e. Now my question is what is the physical justification of only going up to order e and do ...
2
votes
1answer
313 views

Connecting Fermi levels and band diagrams to potential diagrams?

I'm trying to make sense of how you can find the potential diagram given the band diagrams of a few adjacent materials. As a simple example, in semiconducting heterostructures, if you have sandwich ...
4
votes
0answers
71 views

Quantum unscrambling

This question is similar to the Phys.SE post Retrodiction in Quantum Mechanics, however, it addresses a different issue: how would you design a machine that can measure a simple quantum system and "...
6
votes
1answer
757 views

Do spin-spin interactions break time reversal symmetry?

I'm sure the answer is yes, but how is this shown? Normally for a single spin-1/2 you have a time reversal operator: $-i \sigma_y \hat{K}$ where $\sigma_y$ is the second Pauli matrix and $\hat{K}$ is ...
1
vote
2answers
275 views

Rabi oscillation, electron in a box

This page on Rabi oscillation says the Hamiltonian has an interaction term $d \cdot E(t)$, where $d = -$e$r$. (I'm sure what they mean is, that's what the off-diagonal terms of the Hamiltonian look ...
6
votes
1answer
183 views

Faster than light messages (paradox resolution)

I have a thought experiment which in my understanding leads to faster than light messaging, and I had hoped the physics.SE community could help me resolve it. I should say that most of my ...
1
vote
2answers
699 views

Wave function decomposition

Problem: Given the wave function $\Psi_0=A\sin^2(\theta)$ along with the Hamiltonian operator of a physical system: $H=\frac{L^2}{2I}+g B L_z$, find the eigenvalues and eigenfunctions of $\hat{H}$ ...
3
votes
1answer
752 views

Continuous spectrum (quantum mechanics) [duplicate]

Does a continuous spectrum of an observable always imply that the corresponding eigenvectors will not be normalizable? If yes, how to prove it?
1
vote
2answers
2k views

Prove $[A,B^n] = nB^{n-1}[A,B]$

I am trying to show that $[A,B^n] = nB^{n-1}[A,B]$ where A and B are two Hermitian operators that commute with their commutator. However, I am running into a little problem and would like a hint of ...
0
votes
0answers
196 views

Collision of 2 neutrons

If two neutrons collide in 3D space and we want to determine the final velocities of both nuetrons (3 components for each neutrons), we can use the conservation of momentum equations and the ...
1
vote
1answer
123 views

Spinor and Scalar Bose-Einstein condensate

I read about an order paramater that describes a Bose-Einstein condensate. But I don't understand, the classification into "scalar" condensate and "spinor" one. Is it linked with spin of atoms that ...