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 ...

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Is there any operator behind probability, in quantum mechanics?

In Quantum mechanics, the probability of finding a particle at position $x$ is given by $|\psi(x)|^2$, where $\psi$ is the wave function. Wonder what is the operator which gives this probability? Is ...
6
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1answer
238 views

Derivation of neutrino oscillation phase factor

As we know, the neutrino $\nu_{\alpha}$ with flavor $\alpha=e,\mu,\tau$ is a linear combination of mass eigenstates: $$ |\nu_{\alpha}\rangle=\sum_iU_{\alpha i}|\nu_i\rangle,\quad i=1,2,3 $$ where the ...
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0answers
69 views

Dynamical localisation in delta-kicked rotor

The quantum delta-kicked rotor is a common tool for studying quantum chaos. The energy of the rotor increases ballistically when kicking at the Talbot time (resonance) and jumps between zero and some ...
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1answer
99 views

Thomas-Fermin approximation of cold atoms in a harmonic trap

In Bose-Hubbard model of cold atoms, one can use Thomas-Fermi approximation to get a rough number of total particle number. In Thomas-Fermi approximation, the site density is $n(R_i)=(\mu-\kappa ...
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1answer
63 views

Jump Method and the Lindblad Equation

I am studying the time evolution of a density matrix using the Lindblad equation. My initial density matrix is $\rho(0)=|\alpha\rangle\langle\alpha|$, where $|\alpha\rangle$ is a coherent state. Then ...
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7answers
2k views

Why is the application of probability in QM fundamentally different from application of probability in other areas?

Why is the application of probability in quantum mechanics (QM) fundamentally different from its application in other areas? QM applies probability according to the same probability axioms as in other ...
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0answers
44 views

about MS in Theorectial Physics [closed]

I am an undergraduate student (Bachelors of engineering) about to complete my 1st year in the field of Information science and engineering or information technology. I am interested in pure physics ...
2
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1answer
140 views

Does the average momentum vanish for an eigenstate of the simple harmonic oscillator?

Suppose we have a simple harmonic oscillator, let's consider the ground state, $|0\rangle$ and the first excited state $|1\rangle$. $\langle 0|\hat p|0 \rangle$ is zero right? Since the particle can ...
2
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1answer
90 views

Stabilization of von Neumann equation

Given the solution of the Von Neumann equation $\rho(t) = e^{-i H t/\hbar} \rho(0) e^{i H t/\hbar}$ How can we justify if it will be stabilized as $t\rightarrow\infty$ in general? For example, ...
9
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1answer
174 views

What does QM say about the past rather than the future?

In QM, the wave function (in the Copenhagen interpretation) is not an actual physical wave but a device to derive probabilities about the outcomes of experiments. The wave function encodes all the ...
3
votes
6answers
2k views

Is there any relation between Planck constant and Gravitational constant?

Why is the Gravitational constant about $10^{23}$ times of the Planck constant in SI-units? Is there any relation between them? I mean Planck constant is about $6.6\times 10^{-34}$ $Js$ and ...
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4answers
26k views

Stopping potential in the photoelectric effect, collector work function

In this question I am talking about the following situation: Now, I know that the max kinetic energy of the electrons emitted is $KE_{max} = h\nu - e\phi_{em}$ where $\phi_{em}$ is the work ...
2
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1answer
6k views

Relation between electric potential and wavelength of an electron

"An electron that is accelerated from rest through an electric potential difference of $V$ has a de Broglie wavelength of $\lambda$. Investigate the relationship between $V$ and $\lambda$." I had two ...
2
votes
1answer
78 views

Time evolution of states - Is total energy constant or not?

Suppose the state of the particle is given as follows: $$ |\psi_{(t)}\rangle = \frac{1}{\sqrt2} \left( e^{-\frac{i\omega t}{2}} |0\rangle + e^{-\frac{3i\omega t}{2}} |1\rangle \right) $$ Where the ...
3
votes
0answers
470 views

Probability density of Klein-Gordon equation

This may, perhaps, stir some healthy debate; at least I am having some "fun" thinking about it, hopefully I can solicit some outside views too. It is often regarded that the Klein-Gordon equation ...
0
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1answer
88 views

Calculations with operators - Proof: Equation of Operators [duplicate]

I have a problem in Quantum mechanics 1 with Operators. I have to prove the following equation. I tried it for about 4 hours without any result: Condition: $[[\hat A,\hat B],\hat A]=[[\hat A,\hat ...
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2answers
263 views

Quick question on sketching wavefunction in well

Usually for an infinite well, the sketch for n=3 level is this: Now I think if one side of the potential barrier is higher, the particle will be more likely to spend time on the left side than ...
3
votes
3answers
278 views

Stimulated emission and No cloning theorem

I have a little trouble with the simulated emission. I know of the no-cloning theorem which states that it is not possible to duplicate any state. One the other hand, I know about the stimulated ...
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3answers
5k views

How is temperature related to color?

I spent some time studying about temperatures and color of objects. It turns out that as we heat something it turns to red, then yellowish white and if we heat it more it turns to bluish-white. Like ...
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1answer
54 views

Collapse of quantum state upon measurement - why not some other unit scalar multiple

I have learnt that upon measurement, the state of the system changes to the eigenstate corresponding to the observed eigenvalue. Specifically, we obtain the eigenstate that is the normalized ...
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2answers
353 views

Angular momentum - maximum and minimum values for $m_{\ell}$

I want to work out the maximum and minimum values for $m_{\ell}$. I know that $\lambda \geq m_{\ell}$, therefore $m_{\ell}$ is bounded. In the lectures notes there is the following assumption: $$ ...
0
votes
1answer
76 views

Conservation of probability in Jaynes-Cummings model

I was reading about Jaynes-Cummings model. I've studied Bachelor level QM. In the interaction picture the solution with rotating wave approximation and initial conditions $C_g(0)=0$ and $C_e(0)=1$ is ...
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4answers
2k views

Why are hydrogen energy levels degenerate in $\ell$ and $m$?

Is there a good physical picture of why the energy levels in a hydrogen atom are independent of the angular momentum quantum number $\ell$ and $m$?
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2answers
91 views

Do photons in interferometer violate the law of conservation of mass?

I mean Mach-Zehnder Interferometer, where light split into two shortest paths. Is light after splitting wave or particle? Is it a particle? How could one photon change to two? If the wave, does the ...
3
votes
2answers
126 views

Solution of dynamics of density matrix

Given the dynamics of the density matrix: $ \frac{d}{d t}\begin{pmatrix} \rho_{00} & \rho_{01} \\ \rho_{10} & \rho_{11} \end{pmatrix} = \begin{pmatrix} \lambda ...
7
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1answer
1k views

Box normalization

Whenever we study free fields, the solutions of these fields (or particles, whatever feels most comfortable) are always given by plane waves. The dispersion-relation $\omega=\omega(k)$ will of course ...
2
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2answers
478 views

Question regarding Schrödinger's equation

Here is my understanding of Schrödinger's equation and wave functions: (I'm considering the time independent equation.) The equation takes in values of energy as an input and, being a differential ...
2
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2answers
209 views

Wouldn't 3 or more particle entanglement allow passing classical information?

My (simple) understanding of entanglement is that by measuring the spin of one entangled particle, the other entangled particles' spin changes to the opposite of measured particle. This act of ...
3
votes
2answers
555 views

Is quantum uncertainty principle related to thermodynamics?

Would like to ask a question, but first i would like to say Hello Everybody in a way that plays the system, since some geniouses decided that one should not be able to say hello in a question. The ...
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0answers
190 views

Beginner Quantum Mechanics Questions and Theories [closed]

So, I recently read the following article: http://www.preposterousuniverse.com/eternitytohere/quantum/ and I have some questions on some of the things it discussed, as well as some theories of my ...
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1answer
203 views

Nuclear shell model - finite square well

I am trying to make a simplified approximation and solve Schrodinger equation in the finite square well to model the nucleus of Ca (shell nuclear model). The potential is $ V(r) = -V_0$ for ...
1
vote
1answer
41 views

Why the trap is needed in cold atom experiment?

In ultracold atomic gas experiments, the optical lattice provides a periodic optical potential to trap the atoms, why an extra trap, usually a harmonic trap is needed to trap the atoms?
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2answers
231 views

Stationary state of time-independent Schroedinger equation is always real valued function?

I am reflecting on the solution of the time-independent Schroedinger equation. My reasoning is that the stationary state of the time-independent Schroedinger equation must be a real valued function ...
2
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1answer
79 views

Angular momentum of anyons

Why is it true that anyons can have angular momentum taking any real value? Why aren't they restricted to the $j(j+1)$ integer values most are familar with?
3
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1answer
136 views

Electron momentum distribution and wavefunction in momentum space

Does there exist any relationship between the electron momentum distribution used in above threshold ionization and the wave function in momentum space? In other words, starting with the wavefunction ...
2
votes
1answer
2k views

How does temperature affect an electrical current

Synopsis I have read an interesting article J. Halderman et al. "Lest we remember: cold boot attacks on encryption keys" in computer science regarding cold booting. The paper discusses how the use ...
7
votes
2answers
466 views

Time-dependent Schrodinger equation from variational principle

In the paper, "Density-functional theory for time-dependent systems" Physical Review Letters 52 (12): 997 the authors mentioned that the action $$ A= \int_{t_0}^{t_1} \mathrm dt \langle \Phi(t) | i ...
2
votes
1answer
76 views

Alice sends random states in a channel, what Bob receives?

Suppose Alice prepares $\rho_x$ with probabilities $p_x$ and sends it to Bob. I would say this is the same thing as "Alice prepares $\rho = \sum_x p_x \rho_x$ and sends it to Bob", but Preskill's ...
3
votes
1answer
88 views

State with non-zero angular momentum - cannot be described by spherical harmonic?

For a state with non-zero angular momentum, why is it that it cannot be described by the spherically symmetric spherical harmonic?
1
vote
1answer
124 views

Euclidean functional Integrals

In the chapter "Uses of Instantons" from the book "aspects of symmetry" by Sidney Coleman I have come across the euclidean version of the path integral in semi-classical approximation. To evaluate the ...
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1answer
64 views

Atom state vectors kets

An atom with two energy levels has 2 states (excited and ground), represented by kets $|e\rangle$ and $|g\rangle$ respectively. The atom has energy $\frac{1}{2}E_\theta$ when excited and ...
5
votes
2answers
2k views

What does “causally connected” or “causes” really mean?

In a different thread, a user stated the following in respect of events preceding or following other events: However, if the two events are causally connected ("event A causes event B"), the ...
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votes
2answers
185 views

Quantum entanglement and special relativity PARADOX [closed]

Imagine two entangled atomic clocks. After we entangle them, we measure the time: it does has to be the same , right ? Now lets suppose that we entangle them , but don't measure them, then we plant ...
2
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0answers
45 views

How to load Bose-Einstein Condensates into an optical lattice?

In cold atom experiments, what techniques are used to load Bose-Einstein Condensates into an optical lattice??
6
votes
2answers
386 views

Naive questions on Goldstone modes and a possible duality relation?

For example, let's consider a 1D spin-1/2 ferromagnetic (FM) Heisenberg chain $H=-J\sum_{i=1}^{N}\mathbf{S}_i\cdot\mathbf{S}_{i+1}$ with periodic boundary conditions. Now we want to study its low ...
2
votes
0answers
94 views

Continuous Variable Entanglement Measure for the Statistically Mixed State

Can anybody tell me, which is the best entanglement measure for the Continuous Variable Entanglement of a Statistically Mixed State ? I have read that Schmidt decomposition is not valid in this ...
7
votes
1answer
282 views

ket vector with two “entries”

This is a very simple question. I am learning about angular momentum. In my lecture notes, the symbol $|\lambda,m_l \rangle$ was defined as a eigenfunction of a central potential. Two assumptions are ...
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2answers
232 views

details for the double slit experiment

In the double slit experiment with electrons, are all electrons going through the slits? If the electron gun is directed between two slits, than it should hit the central part between the slits, isn't ...
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3answers
274 views

Intuition/derivation behind the probability current definition

The definition is: $${\bf{j}} = \frac{\hbar}{2mi} (\psi^* \nabla \psi - \psi \nabla \psi^*)$$ However: Where ever I have looked, the above "pops out of nowhere". I was wondering how can I obtain ...
2
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0answers
64 views

superposition versus statistical mixture interpretation

I have an interpretation problem here. It is about the coherent state $$\left|\left.\alpha,\frac{\pi}{2\Omega}\right.\right\rangle = ...