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 ...

learn more… | top users | synonyms (4)

0
votes
0answers
194 views

Wave equations for two intervals at Potential step

Lets say we have a potential step as in the picture: In the region I there is a free particle with a wavefunction $\psi_I$ while in the region II the wave function will be $\psi_{II}$. Let me ...
1
vote
1answer
508 views

Can we use intensities in the superposition principle?

In using the superposition principle to calculate intensities in interference patterns, can we add the intensities of the waves instead of their amplitudes? I think that amplitude account for the ...
2
votes
0answers
59 views

Trotter splitting and entanglement entropy

I have heard that a numerical solution to the Schrodinger equation using the Trotter splitting formula for a many-body Hamiltonian can cause an artificial increase in the entanglement entropy. I was ...
17
votes
3answers
1k views

Quantum mechanics - how can the energy be complex?

In section 134 of Vol. 3 (Quantum Mechanics), Landau and Lifshitz make the energy complex in order to describe a particle that can decay: $E = E_0 - \frac{1}{2}i \Gamma$ The propagator $U(t) = ...
0
votes
0answers
40 views

Is it easier to determine the number of states with raising/lowering operators or using scattering?

A particle is bound by $$V(x) = \begin{cases}\infty,& x <0 \\ \frac{-32\hbar^2}{ma}, & x\le a \\ 0, & x \le a\end{cases}$$ a) how many states are there? i'm attempting ...
4
votes
0answers
128 views

Question about the HVZ theorem

In this paper1 the authors cite the HVZ theorem2 saying that it follows from the method used by M. Reed & B. Simon without modifications; I don't really understand this point. Is there anyone who ...
7
votes
2answers
380 views

Why does the quantum Heisenberg model become the classical one when $S\to\infty$?

The Hamiltonian of the spin $S$ quantum Heisenberg model is $$H = J\sum_{<i,j>}\mathbf{S}_{i}\cdot\mathbf{S}_{j}$$ I have read that when the spin quantum number $S\to\infty$, quantum fluctuation ...
6
votes
3answers
1k views

A question on the existence of Dirac points in graphene?

As we know, there are two distinct Dirac points for the free electrons in graphene. Which means that the energy spectrum of the 2$\times$2 Hermitian matrix $H(k_x,k_y)$ has two degenerate points $K$ ...
3
votes
1answer
378 views

Bloch sphere representation

Suppose you know that a qubit is either is in state $|+\rangle$ with probability $p$ or in state $|-\rangle$ with probability $1-p$. If this is the best you know about the qubit's state, where in the ...
1
vote
1answer
2k views

Energies and numbers of bound states in finite potential well

Hello I understand how to approach finite potential well (I learned a lot in my other topic here). However i am disturbed by equation which describes number of states $N$ for a finite potential well ( ...
0
votes
2answers
139 views

EPR vs. EPRBB? Why can't we perform the original EPR experiment?

The EPR gedanken experiment was invented by Einstein Podolsky and Rosen in 1935. It involved positions and momenta. In 1957, Bohm revised this gedanken experiment into one involving spins, or ...
0
votes
2answers
272 views

If inherent randomness exist in quantum mechanics, what then of eternalism implied by relativity?

I am nothing but a curious layman so don't go too technical on me. First of all, I am well aware that a lot of people consider the question of determinism vs indeterminism to be unsolved and others ...
0
votes
2answers
132 views

Why is the energy spectrum continuous for a plane wave when it has energy less than the potential barrier?

Please explain it in the context of this task: we have a potential barrier that looks like $\prod$, with $E<U$. There are 3 regions: 1) no field 2) barrier 3) no field Solution could be ...
3
votes
2answers
355 views

What is wrong with these ways of determining the mean occupation number?

Could anyone point out what went wrong in this argument? Setup: We have a system with 2 energy levels say with energies $0,e$ respectively. We consider the grand canonical ensemble for the system ...
1
vote
0answers
274 views

linear response for a simple harmonic oscillator

Really sorry for this simple question, but I think it will be useful/interesting in general. Consider a quantum simple harmonic oscillator. Add a perturbation $H_I = -\lambda \hat{x}$ Calculate ...
4
votes
4answers
1k views

Does the observer or the camera collapse the wave function in the double slit experiment?

Ok so if we setup a camera before the slit we will find a single photon and will follow through accordingly, likewise by having a camera setup after the slit, we can retroactivly collapse the wave ...
0
votes
2answers
186 views

About Heisenberg uncertainty principle [duplicate]

What would happen if someone invented a way to measure both position and momentum precisely? If it is impossible why?
5
votes
2answers
725 views

What prevents bosons from occupying the same location?

The Pauli exclusion principle states that no two fermions can share identical quantum states. Bosons, one the other hand, face no such prohibition. This allows multiple bosons to essentially occupy ...
1
vote
0answers
35 views

Is there anything to prevent paired-up neutrons from a complete overlap

The reason "neutrons don't overlap", as DarenW explained it, has to do with intricate forces at play that take into account the spins, iso-spins and symmetry of the wavefunctions. However, assume I ...
3
votes
4answers
370 views

Is this statement about quantum mechanics valid?

In Philosophy of Language by William G. Lycan, there are the lines: Even apparent truths of logic, such as truths of the form "Either P or not P", might be abandoned in light of suitably weird ...
1
vote
1answer
188 views

Is a blackbody real or imagined?

In my reading of blackbody radiation I am always asked to imagine this or that body being a perfect absorber or emitter of radiation, and I am always left with the impression that a blackbody exists ...
4
votes
1answer
959 views

Bohr-van Leeuwen theorem and quantum mechanics

Preamble: If one considers an ideal gas of non interacting charged particles of charge $q$ in a uniform magnetic field $\mathbf{B} = \mathbf{\nabla} \wedge \mathbf{A}$, then the classical partition ...
3
votes
1answer
261 views

Show that for QM operator A: $\int_{-\infty}^{\infty}\psi A^{\dagger}A\psi dx = \int_{-\infty}^{\infty}(A\psi)^*(A\psi)dx $

I need to show for $$A = \frac{d}{dx} + \tanh x, \qquad A^{\dagger} = - \frac{d}{dx} + \tanh x,$$ that $$\int_{-\infty}^{\infty}\psi^* A^{\dagger}A\psi dx = ...
3
votes
3answers
209 views

Curious relation between the dependance in ℏ of Planck units and units dimensions

Looking at Planck units, there seems to be a curious rule between the dependance in $\hbar$ of a Planck unit and the unit dimensions of the corresponding physical quantity. Let the dimensions of the ...
6
votes
4answers
610 views

Interference and which-path information

My understanding is that in a double-slit experiment, quantum interference disappears if which-path information is available. How is available defined? Consider the following experiment: SPDC is used ...
3
votes
1answer
187 views

First order coherence through double slit

The state $$|\Psi \rangle = |0\rangle + \sum_j \int d\omega f_j(\omega)\hat{a}^\dagger_j (\omega) |0\rangle $$ is coming from a far field and incident on a double slit setup. Here j is the index of ...
2
votes
1answer
192 views

Coordinate representation of quantum ladder operator?

I can't seem to figure out how to derive the coordinate representation of the $a_+$ ladder operator in quantum mechanics. I know that $a_-$ is $\sqrt{\frac{1}{2mwh}} (mwx + i\dot{p}) $ in which where ...
2
votes
2answers
1k views

Plotting $\psi$ for finite square well potential

Lets say we have a finite square potential well like below: This well has a $\psi$ which we can combine with $\psi_I$, $\psi_{II}$ and $\psi_{III}$. I have been playing around and got expressions ...
1
vote
1answer
668 views

Finite potential well - transcendent equation for even solutions

I have a finite square well like the one on the picture below: I have done some calculations on it and got a transcendental equation for even solutions which is like this: $$ ...
1
vote
0answers
55 views

exponential potential quantization [duplicate]

What are the energies $E_{n}$ of the Schroedinger operator $$ -\frac{d^{2}}{dx^{2}}y(x)+ae^{bx}y(x)=E_{n}y(x) $$ for some real and positive 'a' and 'b' with the Boundary conditions $ ...
0
votes
2answers
167 views

Probabilistic vs Statistical interpretation of Double Slit experiment

Why is it assumed that the results seen in the double slit experiment are probabilistic and not just a statistical result of some unknown variable or set of variables within the system.
1
vote
0answers
66 views

How does a photon leave trace of its polarization state in a photon detector but not trace of which direction it came in?

Some quantum erasure experiments involve polarization of photons. In one such experiment with a double slit, a horizontal polarizer is used in front of one slit, and a vertical polarizer is used for ...
4
votes
1answer
295 views

double slit experiment with two opposite quarter waveplates

Consider the usual double slit experiment involving laser and a double slit and a screen. Now place in front of the left slit a quarter waveplate (let's call it QWP1) that changes a certain linear ...
1
vote
1answer
142 views

Quantum Mechanics of Lenz's Law?

I've searched the internet and two famous QM books (Sakurai and Messiah) for Lenz's Law, but haven't found anything. So my question is what the quantum mechanical explanation to Lenz's law is? Can ...
0
votes
1answer
163 views

Does quantum reversibility require many worlds?

The source S sends a photon into the beam splitter below. There is a 50% chance that it will be detected at A and a 50% chance it will be detected at B. ...
2
votes
2answers
210 views

Indistinguishable particles in quantum mechanics

If you have two particles of the same species , Quantum mechanics says that $\Phi_{m_{1},x_{1},p_{1},m_{2},x_{2},p_{2}}=\alpha\Phi_{m_{2},x_{2},p_{2},m_{1},x_{1},p_{1}}$ But I don't understand why ...
7
votes
2answers
665 views

Meaning of spin

I'm pretty astounded that I did not hear about this sooner, but in my course on QFT our professor told us that the concept of spin can be used to mean three things: Mechanical spin (apparently a ...
2
votes
2answers
185 views

Von Neumann Entropy: varying definitions

I have seen different authors define von Neumann entropy in different ways. In particular, some use the natural logarithm and others log to base 2. What is the reasoning for this? Does it make any ...
0
votes
1answer
195 views

Identical fermions in the same quantum state

If we are to take two Hydrogen atoms and subject them to the same potential, then wouldn't both Hydrogen atoms be in the same exact quantum state? This bother me because no two identical fermions can ...
1
vote
1answer
831 views

Finite, square, potential well

Lets say we have a finite square well symetric around $y$ axis (picture below). I know how and why general solutions to the second order ODE (stationary Schrödinger equation) are as follows for ...
3
votes
1answer
178 views

Force analysis of silver atom in Stern–Gerlach experiment

In this experiment we only consider the force at z direction, but $\vec B$ field gradient doesn't exclusively exist at z direction according to Maxwell's equations. So why don't we see the splitting ...
1
vote
1answer
242 views

Definition of energy

What is the definition of energy $E$ given a dispersion relation $\omega=\omega(k)$ where $k=|\vec k|$ and $\omega$ is not necessarily linearly proportional to $k$? What about momentum $\vec p$? This ...
0
votes
2answers
291 views

Finite square well

I know how and why we use this form of stationary Schrödinger equation for finding $\psi$ outside the finite square potential well: $$\frac{d^2 \psi}{dx^2}=\kappa^2 \psi$$ I Also know that the ...
3
votes
2answers
339 views

Schmidt basis: Entanglement

I do not understand how any state in Hilbert Space $\mathcal{H}=\mathcal{H}_A\otimes\mathcal{H}_B$ of dimension $\text{dim}(\mathcal{H}_A)\times\text{dim}(\mathcal{H}_B)$ can be decomposed in the ...
2
votes
2answers
227 views

What does the Copenhagen interpretation say about the position of a particle before measurement?

Suppose there is a particle in space. When we measure the position of that particle, we get a particular value with a probability that can be calculated from the wave function. But, according to the ...
0
votes
3answers
320 views

Is normalization consistent with Schrodinger's Equation?

Schrodinger's Equation does not set a limit on the size of wave functions but to normalize a wave function a limit must be set. How is this consistent physically and mathematically with Schrodinger's ...
3
votes
1answer
110 views

Prove an action expansion's even-indexed terms have to be integrated, where the odd-indexed terms are only derivatives of the potential (WKB)

After assuming a wavefunction of a form: $$ \psi \approx A \exp{\left(i \frac{S(x)}{\hbar}\right)}$$ and letting $$S = \hbar^0 S_0 + \hbar^1 S_1 + \hbar^2 S_2 +...$$ The odd-indexed terms of the ...
4
votes
1answer
157 views

Semi-conductors

Suppose there is a semiconductor with Fermi energy $E_f$ and that there are $N$ bound electron states. I'd like to know why the mean number of excited electrons takes the form $$\bar n={N\over ...
5
votes
5answers
338 views

Derivation of $ E=h\nu$

Is it possible to derive the relation $ E=h\nu$ from Schrodinger equation or the basic principles of quantum mechanics or is it something which is considered to be an axiom with no explanation?
16
votes
3answers
886 views

Does quantum computing rely on particular interpretations of quantum mechanics?

It is my understanding that quantum computing relies on quantum superposition and entanglement to work--qbits must exist in all states simultaneously before giving a particular result when observed. ...