# Tagged Questions

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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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)...
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 ...
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 ...
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 ...
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### 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, ...
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### 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,...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
1answer
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### 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 ...
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 $\langle V\rangle$ ...
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 ...
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 ...
2answers
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### 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 ...
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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 ...
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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 ...
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 ...
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 ...
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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 ...
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 ...
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. ...
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 ...
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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 ...
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 ...
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 ...
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 ...
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 ...
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### 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 ...
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 ...