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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1answer
46 views

Relation between Von Neumann entropy (and other entanglement measures) and thermodynamical entropy

Suppose I have a bipartite system (with Hilbert space $H = H_a \times H_b$) and the following state: $$\sigma = \sum_{n} \frac{e^{-\beta E_n}}{Z} \rho_n$$ where $Z = \sum_n e^{- \beta E_n}$ and ...
1
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2answers
108 views

Uncertainty principle in quantum field theory

Can the uncertainty principle be derived in quantum field theory? If yes, does is have a different interpretation than quantum mechanics because the coordinates $x_i$ are now parameters and not ...
2
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1answer
89 views

Probability current in scattering problems

This is a section from Wikipedia: In regions where a step potential or potential barrier occurs, the probability current is related to the transmission and reflection coefficients, respectively ...
13
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6answers
5k views

How is quantum superposition different from mixed state?

According to Wikipedia, if a system has $50\%$ chance to be in state $\left|\psi_1\right>$ and $50\%$ to be in state $\left|\psi_2\right>$, then this is a mixed state. Now consider state ...
3
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1answer
198 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 ...
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0answers
44 views

Electron energy in magnetic field

For a problem early in a book I'm reading (Quantum Mechanics by Albert Messiah), I'm asked the following: Consider an electron following a circular trajectory in a constant magnetic field $H$ (I'm ...
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2answers
90 views

Is every bra vector the complex conjugate of ket vector?

$\renewcommand{\ket}[1]{\lvert #1 \rangle}\renewcommand{\bra}[1]{\langle #1 \rvert}$Suppose we are taking the inner product of two vectors, say $a$ and $b$ as $$\bra{a}b\rangle$$ where $\bra{a}$ is a ...
3
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2answers
887 views

Why are eigenfunctions which correspond to discrete/continuous eigenvalue spectra guaranteed to be normalizable/non-normalizable?

These facts are taken for granted in a QM text I read. The purportedly guaranteed non-normalizability of eigenfunctions which correspond to a continuous eigenvalue spectrum is only partly justified by ...
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4answers
300 views

Is it possible for two events happen at the exact same time?

Is it possible for any two thing to occur at the exact same time? As I see it, because time can always be split up into smaller units (it is infinitely divisible), we can always be more and more ...
0
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1answer
33 views

How is measurement on system in a Hilbert space seen?

I am a bit confused about different kinds of measurements on a system in state $W$ where $W$ is the density operator in Hilbert space $H$. A general measurement can be given by POVM's, let ...
0
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1answer
47 views

Property of the wave functions of a free particle

How can I show that the following holds? $$\langle nlm\mid \partial_z^2\mid nlm\rangle=-\int_0^{4\pi}d\Omega\int_0^{\infty}drr^2\left|\partial_z\psi_{nlm}\right|^2$$ The wave functions of a free ...
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0answers
19 views

Can I use the Chi squared test to see if my data fit to the Wigner-Dyson distribution indicating chaotic behaviour? [migrated]

I recently read the paper about Quantum Chaos in Feshbach resonance spectra of ultracold Erbium [1]. The authors analyze their data statistically using the random matrix theory framework for ...
0
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0answers
20 views

Why is it necessary for all the component-states to have same phase for interference?

I am currently reading Decoherence. In this site, it is written : Now here is the absolutely key point: every component eigenstate has an associated phase . It is this phase$^1$ which gives the ...
9
votes
4answers
344 views

Seeking a quality plain-language description of the Wigner-Eckart theorem

I'm a third year physics undergrad with a very cursory knowledge of quantum mechanics and the formalism involved. For instance, I understand roughly how tensors work and what it means for a tensor to ...
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3answers
133 views

What can change a photon's frequency?

I found this question: Is it possible to apply force to a light particle? As it states, gravity can change the frequency of light by changing its momentum. My question regards other phenomena that ...
2
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2answers
108 views

Time evolution of a wavepacket

I do not understand why if $H\psi = E\psi$, then the time-evolution of the wavefunction is given by $e^{-iEt/h}\psi(x)$.
4
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3answers
417 views

Why doesn't Many-Worlds interpretation talk about many worlds?

I was reading this interpretation from this site, where these lines are noteworthy enough to talk for the fact that this interpretation doesn't actually talk about many-worlds: These are the "many ...
2
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2answers
289 views

Many-worlds interpretation vs 'just' randomness?

I have this question about MWI I always wanted to ask but never dared to! It could be that I just don't know enough physics to understand the answer, or the question! Anyway, here goes: What is it ...
0
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0answers
28 views

Position operator for wave function of entangled system? [on hold]

When I read about EPR paradox, I have the following confusion. Consider the whole system, it is a pure state, so it can be described by a wave function. (For sub-system(one of the electrons), it is ...
2
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1answer
105 views

Quantum fluctuation

According to the quantum fluctuation concept, a particle and its corresponding antiparticle appear out of nothing only to annihilate and emit some energy in the form of electromagnetic waves. Does ...
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2answers
51 views

How long does it take for an excited electron to return to ground state?

During a mock Cambridge interview, one of the questions was about how small a computer could theoretically be.The way I approached it was in terms of what something must be to be considered a ...
2
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0answers
42 views

Interpretation of the diode constant in a LED

For a real diode the current as function of the potential difference between its terminals (for big enough voltage) is given by: $$I=A e^{\frac{eV-E}{\eta k_B T}} \tag{1}$$ So in the case of LEDs ...
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0answers
47 views

Quantum Mechanics - Induction Methods [closed]

Let $a$ be a lowering operator and $a^\dagger$ be a raising operator. Prove that $$a(a^\dagger)^n = n (a^\dagger)^{(n-1)} \, .$$ My professor suggested to use induction method with formula: $$\left( ...
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1answer
265 views

Wigner Threshold law in Photodetachment and Photoionization

I am writing this question here because I have a problem in understanding the Wigner Threshold law in Photodetachment and Photoionization. The Wigner Threshold Law is given by: $\sigma$=$E^{L+1/2}$. ...
7
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1answer
180 views

spooky nonlocal communication, or bad abstract?

I'm referring to this recent paper, "Experimental Proof of Nonlocal Wavefunction Collapse for a Single Particle Using Homodyne Measurements" by Fuwa et al. published in Nature Communications. ...
0
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1answer
32 views

What is the form of the kinetic energy operator on a one dimensional (real space) lattice? (In second quantization)

I'm trying to figure out how one would write down the hamiltonian of a free fermion system (eventually in second quantization) on a one dimensional lattice and I'm having trouble both coming up with ...
2
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1answer
88 views

What do we mean by “typical state”?

My question is somehow simple, but not trivial. I'm reading many articles about the ER=EPR correspondence. There are some articles which study this proposal from a field theory point of view (one ...
5
votes
1answer
93 views

Quantum Mechanics - Lowering Operator [closed]

Let $a$ be a lowering operator. Show that $a$ is a derivative respects to raising operator, $a^\dagger$, $$a = \frac{\textrm{d}}{\textrm{d}a^\dagger}$$ Can someone please explain how to prove the ...
0
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1answer
63 views

What is the recent most important discovery and study about magnets? [closed]

I believe that magnetism is a very powerful tool to do various things.It can make amazing machines.What is the recent most important piece of study that has been done of magnetism. The study that can ...
0
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1answer
33 views

Energy of a system if the nuclear repulsion increases

I have calculated the optimised geometry for a molecule. I have noticed that the energy of the nuclear repulsion increases with each iteration of optimisation. What is the logic behind this?
-2
votes
1answer
41 views

Simple question about using determinant to find eigenvalues of $\hat{S_x} + \hat{S_y}$ [closed]

The problem is: Find the eigenvalues and eigenfunctions of the operator $\hat{S_x} + \hat{S_y}$ where $\hat{S_i}$ is the spin operator in the i direction (i = x,y,z). The first step of their ...
9
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5answers
1k views

Intrinsic structure of electron

The electron contains finite negative charge.The same charges repel each other.What makes electron stable and why does it not burst? Is it a law of nature that the electron charge is the smallest ...
0
votes
1answer
43 views

Theoretical proof of the Bohr's postulates

It was proved in an experimental way that the energy of a photon equals $E = h \nu$ electrons radii satisfy the equation $mvr = n \hbar$ Is it possible to prove these properties in a theoretical ...
13
votes
1answer
460 views

How to evaluate this sum of coupling coefficients?

I would like to evaluate the following summation of Clebsch-Gordan and Wigner 6-j symbols in closed form: $$\sum_{l,m} C_{l_2,m_2,l_1,m_1}^{l,m} C_{\lambda_2,\mu_2,\lambda_1,\mu_1}^{l,m} \left\{ ...
0
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0answers
23 views

Collision between electrons & nucleus [duplicate]

I am new with physics and I have a confusion that since electron and nucleus has opposite charges then why they do not collide with each other inside an atom?
1
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2answers
73 views

What is the nature of the state of a 2 particle system?

If I want do describe two particles #1 and #2 within Quantum Mechancis - let them be different in some way (Spin for example) - how do "I" decide if the total state of the system should be an ...
18
votes
3answers
734 views

How is quantum mechanics compatible with the speed of light limit?

Consider a free electron in space. Let us suppose we measure its position to be at point A with a high degree of accuracy at time 0. If I recall my QM correctly, as time passes the wave function ...
0
votes
1answer
122 views

Slit width for minimum spot size in electron slit diffraction if involving uncertainity principle

I don't believe the following is an accurate description of the physical but a homework problem to help understanding. A beam of electron of energy 0.025 eV moving along x-direction, passes ...
1
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1answer
184 views

Impulse travelling faster than light

There have been conducted many experiments in which light impulses traveled faster than light like the one in Princeton in 2000. This phenomenon has something to do with quantum entanglement. Does ...
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3answers
59 views

Two questions about Variational Method of quantum mechanics

I have two question about variational method of quantum mechanics. Why we always find the ground state energy by this approach. Why not the other excited states? When we find the ground state energy ...
0
votes
1answer
82 views

Operators is a infinite dimensional matrix, how can it multiply by a wave function that is a n*1 (n is finite) matrix

My confusion started from thinking the quantum superposition principle. Several website say that the quantum superposition means all state can be represented as infinity superposition of orthogonal ...
0
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0answers
201 views

Semiclassical approximation for the exponential sum (partition function)

For any real and positive $s$ and in the sense of semiclassical approximation, is this valid? $ \sum_{n}exp(-sE_{n})\sim \iint_{C}dxdpe^{-s(p^{2}+V(x))}$ valid for every $s$ Here simply both the sum ...
0
votes
1answer
108 views

Understanding an equation in quantum mechanics (J. J. Sakurai, “Modern QM”, eq. 2.3.13) [closed]

Hello, It is from quantum mechanics book of sakurai. You can see equation 2.3.12b implies 2.3.13. But my question is, how? Could you please show me how can i bring equation 2.3.13 from 2.3.12b ...
1
vote
1answer
144 views

How is quantization related to commutation? [duplicate]

How are commutation (of observables) and quantization related? Reading about the Stone-Von Neumann Theorem, it seems that commutativity is the classical limit of quantum mechanics, and hence ...
0
votes
1answer
31 views

Entanglement and Special Relativity [closed]

There are 2 particles entangled and move far apart to 2 measuring devices . The first measurement of either particle will collapse the wave function and set spin up and spin down on the particles. 2 ...
0
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0answers
31 views

The relation between commutation and quanta

This question discusses discretization in some sense, and this question talks about how quantization and Hilbert Spaces are related (the answer seems to to be not at all), but what I'm curious about ...
12
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1answer
434 views

What is the probability of quantum tunneling occurring in this CPU?

You may have noticed over the last few years that Moore's law is no longer applying to the real world. This observation states that over the history of computing hardware, the number of transistors on ...
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0answers
28 views

Can anybody recommend a book on quantum physics for a mathematically minded student? [duplicate]

Basically what the title says. I'm a math/physics double major going into my second year, but I'm much more math oriented. I'll be taking a quantum class in the fall and I'd like a book that ...
0
votes
1answer
51 views

Does Quantum mechanics predict (statistical) frequencies?

I began reading a book by Bricmont and Zwirn (Philosophie de la mécanique quantique, as yet not translated). In a note (page 4), Bricmont writes (translation mine): Probability is a theoretical ...
0
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1answer
137 views

Does a normal torch emit entangled photons?

I was reading a sciencenews.org post about three photons being entangled. My question here is, why is the chance of producing an entangled pair once in a billion times? Isn't every particle produced ...