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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208 views

How to understand wavefunction in quantum mechanics in math

I am reading some introduction on quantum mechanics. I don't understand all but I get the point that the wavefunction tells some probability aspects. In one book, they show one example of the ...
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1answer
2k views

How to find the wavefunction that solves an infinite square well with a delta function well in the middle?

Solutions for the wavefunction in an infinite square well with a delta function barrier in the middle are easily found online (see here for an example). I am wondering what the wavefunction is for an ...
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3answers
521 views

Why is it difficult to differentiate between interference and diffraction?

Why is it difficult to differentiate between interference and diffraction? Is it because we don't clearly understand how both of these phenomenon takes place? My thoughts: From an answer to one of ...
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5answers
342 views

Do orbitals overlap?

Yes, as the title states: Do orbitals overlap ? I mean, if I take a look at this figure... I see the distribution in different orbitals. So if for example I take the S orbitals, they are all just ...
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2answers
126 views

How does interaction of a system with the environment lead to the damping of interference terms?

A general way to describe a system $S$ that is entangled with an environment $E$ is $\rho_{S}=Tr(\rho_{SE})=\sum\limits_{m,n}c_mc^*_n |s_m\rangle \langle s_n| \langle e_n|e_m\rangle$ with ...
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1answer
305 views

Quantum Mechanics and the Airy Function, the physics of the turning point

I'm working with the Airy function, and the book states at $x=0$ is a turning point, and there are two very different behaviors on either side. In general what a does a turning point mean in ...
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1answer
61 views

Can entanglement with an inaccessible system be useful?

Quantum phenomena in bipartite pure state systems like teleportation are pretty well understood. What I'm interested in is the following situation: Alice, Bob and Charlie hold some general tripartite ...
2
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2answers
284 views

Why is Quantum Teleportation important in Cryptography?

I think the physical principle is that (Wikipedia): For every qubit teleported, Alice needs to send Bob two classical bits of information. These two classical bits do not carry complete ...
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1answer
236 views

Quantum harmonic Oscillator analytic method

I'm using a book from Griffiths, I got really stuck about how he arrived at the approximate solution, is it just by trying( trial solution method?), I really appreciate any help on this. ...
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1answer
244 views

How deep is the region near an event horizon where Hawking radiation is generated?

In other words, how strong does gravity have to be to cause Hawking radiation to occur?
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1answer
619 views

Momentum variance in momentum space for particle in a box

My assignment asks me to compute the momentum space wavefunction of the nth energy eigenstate of the particle in a one-dimensional infinite square well, then "show that your result is in agreement ...
3
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1answer
124 views

Superpositions with two observers

This is a bit of an odd question. I'm not a physicist, so bear with me if I say something wrong. Lets say you have some sort of quantum event where matter is in a superposition. Standing next to you ...
3
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1answer
316 views

Path Integral on a circle (calculation of phase and linear independance)

I am reading Schulman's "Techniques and applications of path integration" chapter on Path integrals on multiply-connected spaces. In the first section he calculates the path integral of a free ...
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4answers
427 views

Experimental evidence of Pauli's exclusion principle

A fermion is described by a set of quantum numbers, this set of numbers lead us to a unique wave function. If two fermions are described by the same wave function (violating the Pauli's exclusion ...
4
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1answer
192 views

Question on conserved quantities and Noether's theorem

I have a question about Noether's theorem in the context of QM, which I'll state in the context of the weak interaction but the basic point could be generalized. According to Noether's theorem, given ...
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0answers
300 views

QM Question about the Dirac Delta Potential

I just wrote down the solution for the bound state of the Dirac delta potential well, for $E<0$, and apparently there is only one specific energy for the bound state, and it is negative. I solved ...
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2answers
106 views

Why is it energetically favourable for molecular bonds to form from a QM point of view?

For example, if you have two hydrogen atoms and an oxygen atom, they are all electrically neutral and don't attract each other. But then if they manage to get "close enough" somehow they snap together ...
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1answer
168 views

Degeneracy in n-dimensional potential well

Knowing that degeneracy occurs in n-dimensional infinite potential well where two wave functions correspond to the same energy, can the same be said for the finite potential well?
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1answer
162 views

Classically, how can an electron orbiting a proton radiate given its relativistic energy

In classical relativistic Electrodynamics, we are often told that any accelerating point charge inherently radiates (Bremstrallung). (This is the basis for the need for a QM conception of electrons.) ...
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1answer
258 views

Given wave function at $t=0$, what is the process of deriving time dependent wave equation? [closed]

Suppose $$\Psi (x, t=0)=Ae^{i\alpha _1}\psi _1(x)+Be^{i\alpha _2}\psi_2(x)+Ce^{i\alpha _3}\psi_3(x).$$ If $\psi _n$ are the energy eigenfunctions how would I derive $\Psi (x,t)$? I am having trouble ...
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1answer
974 views

Overlap integral and probability

I have a question regarding how to extract probability from an overlap integral. Specifically, I am calculating the probability of a particle in a bound state in a delta potential $V=-\alpha ...
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0answers
42 views

What is a good target to aim for when teaching myself quantum mechanics? [duplicate]

I'm interested in teaching myself quantum mechanics, and I'm looking for a good goal to aim for. I've got an undergrad maths degree and a graduate degree in probability theory and stochastic ...
3
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2answers
230 views

Why does the Dopfer EPR experiment require coincidence counting?

Dopfer Momentum-EPR experiment (1998) seems to provide a interesting tweak in the EPR experiment. To read more details on this experiment, see: ...
3
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1answer
97 views

Analytic expression for non-trivial commutators

Motivated by a previous question, consider bosonic creation/anihilation operators $a, a^+$ such that $[a, a^+]=1$, and $N = a^+a$. Is there an analytic expression for the following commutators: ...
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2answers
139 views

Stern-Gerlach and Hund's second rule

According to Hund's second rule, the spin tends to be maximal. That would, in my understanding, imply that, regarding the Stern-Gerlach experiment, the important electron in a silver atom has spin ...
2
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0answers
86 views

Is everything in the universe discrete? [duplicate]

When beginning my education, I regarded nearly everything as continuous and analog in nature: Physical objects could have any mass on a continuous scale Light sources could emit any intensity of ...
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3answers
407 views

Simple Quantum Mechanics Question about The Commutator of Translation Operators

Say there is $\hat{J} = \exp[-i \hat{p} l/ \hbar]$ and $\hat{U}= \exp[-i\hat{H}t/ \hbar]$, where $\hat{H}$ is time-independent. Can we say anything about $[\hat{J},\hat{U}]$? Is it zero? How do we ...
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2answers
474 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 ...
2
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1answer
79 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
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1answer
192 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 ...
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1answer
299 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 ...
2
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1answer
305 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
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1answer
157 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}( ...
6
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1answer
714 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 ...
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2answers
108 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
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1answer
109 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). ...
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0answers
132 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 ...
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1answer
154 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 ...
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3answers
1k views

Average Energy of the Quantum Harmonic Oscillator

In Griffiths, the average potential energy for the quantum harmonic oscillator is given as $$<V>=\frac{1}{2}\hbar \omega(n+\frac{1}{2})$$ Is the potential energy of the quantum harmonic ...
6
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1answer
361 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 ...
7
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3answers
615 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 ...
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2answers
335 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 ...
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0answers
53 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 ...
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1answer
615 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
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1answer
239 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
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1answer
178 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 ...
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2answers
364 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 ...
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3answers
65 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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0answers
120 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 ...
2
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2answers
140 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 ...