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

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 ...
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1answer
41 views

Total angular momentum operator

How do the eigenfunctions of the total angular momentum operator analytically look like? I mean the operator is given by $J = L+S$ so the eigenfunctions have to be tensor-product states, right? Can ...
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0answers
30 views

Why doesn't a quantum pairwise Hamiltonian couple states in which more than one interaction occurs?

This question is about the standard quantum mechanical pairwise interaction Hamiltonian. I'll phrase it in terms of an example using Rydberg atoms, but you could just as well imagine spins (for ...
11
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4answers
1k views

Entanglement, real or just math?

I'm new here, actually this is my first question so I'll just get to it. In quantum entanglement when something acts on one particle the other one reacts also, just in reverse (more or less). From ...
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2answers
68 views

Why isn't the Time-Independent Schrödinger Equation an equation of motion?

I thought an equation of motion was something where you are given a Lagrangian and, using the Euler-Lagrange equation, you then find the equations of motion for that system. Same basic idea for the ...
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0answers
41 views

Why did the universe have a low entropy at the big bang?

Sean Carroll, in his book "From Eternity to Here", asks the following question. Why did the universe have a low entropy at the big bang? in John Cramer version of the Wheeler - Feynman absorber ...
3
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2answers
70 views

Slowing down the double slit experiment

Towards the end of the following video https://www.youtube.com/watch?v=GzbKb59my3U the double slit experiment is executed with 'single' photons and it is shown how the interference pattern emerges as ...
0
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1answer
50 views

Requirements prior to Quantum Mechanics [duplicate]

What are the requirements in physics and mathematics that somebody must have in order to start learning Quantum Mechanics by himself?
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71 views

Is Dirac's quantum mechanics book good for beginners? [closed]

I have not read any other QM books, I have little knowledge on that subject and want a books that uses mathematics in academic levels but is easy to get the grips on and also builds intuition and ...
0
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1answer
41 views

Apply Hamiltonian to position eigenstates

Let $\hat{H}$ be the free Hamilton operator, is it then true that $$\langle {\bf r}| \hat{H} ~=~ - \frac{\hbar^2}{2m} \Delta \langle {\bf r}|~?$$ Where $\Delta\equiv \nabla^2$. I currently don't see ...
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1answer
75 views

Prove that this operator is unitary

$\hat{O}\equiv(1/\sqrt{2\pi})\int e^{-iNz}dz$ $\hat{O}^\dagger\equiv(1/\sqrt{2\pi})\int e^{iN'x}dx$ We have the operator $\hat{O}$ and its Hermitian adjoint $\hat{O}^\dagger$, in the one dimensional ...
2
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1answer
50 views

Help in solving Schrödinger equation for Hydrogen

I have almost finished getting the solution to the Schrödinger equation for the hydrogen atom (got the theta and phi component equations), but am stuck on the r component equation. Can anyone help me ...
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1answer
45 views

How do I take take the partial derivatives of the general solution to the TDSE for a free particle? [on hold]

Consider the general solution to the time-dependent Schrödinger equation for a free particle \begin{align*} \Psi(x,t) &=\frac{1}{\sqrt{2\pi}}\int_{-\infty}^{+\infty} \phi(k) e^{i\left(\hbar ...
2
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1answer
68 views

Expressing the Schrödinger equation in terms of spinors

I appreciate that the Dirac equation can be thought of in terms of spinors, as it directly implies the presence of spin, in addition to initiating the concept of treating fields as operators. From ...
0
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0answers
19 views

Singular points of an orbit space

I am wondering what, precisely, the singular point of an orbit space is. Specifically, I am looking at quantum statistics and the orbit space $M^N/S_N,$ where $M^N$ is the classical configuration ...
0
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0answers
37 views

Fourier Transforming a $n$-dimensional ket (QM)

I would like to evaluate the Fourier Transform of $n$ functions. I am aware from the derivation of the convolution how this is done for the case of $n=2$. How could this be generalised for $n=3$? ...
2
votes
2answers
83 views

Double slit experiment paradox

Two observers – A & B - conduct a single double slit experiment and watch the same detector screen for the appearance of an interference pattern. A separate detector records which slit each ...
2
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2answers
116 views

Flaw in Einstein's explanation of the photoelectric effect?

The essence of Einstein's idea is like this: if a system is in some bound state with energy $-E_b$ with $E_b> 0$ (the threshold of the continuum band is taken as zero), and we drive the system ...
0
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1answer
18 views

What is the reduced width amplitude of an unstable state?

Particularly used in nuclear physics when describing the lifetime (i.e. partial decay width) of a resonant state (a.k.a resonance) is the term "reduced width amplitude". I have searched online, and ...
2
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1answer
34 views

Can someone clarify what should and should not be an operator in my verification of the 1D solution to the SE for a free particle?

I just worked out the 1D free particle solution to the Schrödinger equation. My wave function was \begin{equation} \psi(x,t) = Ae^{i(px-Et)/\hbar} \end{equation} So I plugged this into both sides ...
1
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0answers
47 views

Simultaneous eigenket

J. J. Sakurai states in his "Modern Quantum Mechanics", this fact as a theorem ($\pi$ is the parity operator): Suppose $$[H,\pi]=0$$ and $| n>$ is a nondegenerate eigenket of $H$ with ...
0
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1answer
32 views

Atomic transition involving two electrons

In the Helium-like Iron ion, Fe XXV, there is a transition from $1s2p$ to $2s^2$, and the energy of the two levels are measured as 6667.5686 eV and 13546.26 eV. It seems like this transition involves ...
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1answer
39 views

What's the difference between NMR and EPR?

Both NMR and EPR describe the response of magnetic spin to external field. When collecting data, how do you know you're looking at nucleus spin flip or electron spin flip? In other words, since every ...
0
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1answer
64 views

The meaning of a good quantum number

My book runs through the following argument: Ehrenfest's theorem states that $$\frac{d\langle Q \rangle}{dt}=\frac{[Q,H]}{i\hbar}+\langle \frac{\partial Q}{\partial t} \rangle$$ and so for a time ...
2
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4answers
68 views

Dual of the TDSE

Quite a quick and hopefully simple question. The TDSE takes the form $$i\hbar\frac{\partial\lvert\psi\rangle}{\partial t}=H\lvert\psi\rangle$$ and so if we take the dual of this to find the time ...
0
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1answer
31 views

How do I find the average kinetic energy and average potential energy of a hydrogen electron in the ground state?

In my modern physics class, we are wrapping up the 3D Schrödinger equation, and I am more than a little lost. A few chapters ago, we learned about operators, and I have an equation for both these ...
0
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1answer
53 views

Boundary of classical and quantum world

So we know that for the really small world we have quantum mechanical behavior and for big things we have classical behavior. But what is the boundary that differentiates the two? If we make a thought ...
0
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1answer
18 views

Excitation energy of carotene using the particle in a box model

I'm practicing for an exam and I came across the following question: The linear, conjugated π-electron system of a carotene molecule comprises 11 atoms and the distance between two atoms is 1.4 Å. ...
1
vote
1answer
113 views

Hartree-Fock: Coulomb integral [closed]

Today I was wondering how to better understand the Coulomb integral in the Hartree-Fock approximation. Extracted from: Szabo & Ostlund, Modern Quantum Chemistry, p. 112 The Coulomb term has ...
0
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2answers
44 views

Vector model of addition of angular momenta

I'm trying to understand what Landau and Lifshitz mean in their $\S31$ of "Quantum mechanics. Non-relativistic theory" about vector model of addition of angular momenta: ... This result can be ...
1
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1answer
36 views

Average Energy of a coherent state

The question is relating to a previous problem concerning the harmonic oscillator. Determine the average energy < E > in a coherent state |alpha>. From my understanding the expectation of the ...
1
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0answers
40 views

Hamiltonians on tensor product states

Solid state & Atomic Physics. The wavefunction for the electrons is $\psi(\mathbf{r}, \mathbf{R})$, where $\mathbf{r}$ is the position of the electron and $\mathbf{R}$ of the nucleus. The ...
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4answers
158 views

Derivation of Schrödinger equation - free particle

I learn quantum physics from Alonso-Finn's book (Amazon link), there's one step of Schrödinger equation for a free particle that I couldn't understand. $$ \frac{\mathrm{d^{2}\Psi } }{\mathrm{d} ...
2
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0answers
21 views

Classical and semi-classical vs quantum interferometry

What is the difference between classical, semi-classical and quantum interferometry? How the detectors look like? As far as I know in classical interferometry light is treated as a wave, whereas in ...
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1answer
129 views

Thought experiment on graviton breaking the speed of light [closed]

The effect of gravity travels at the speed of light. Suppose we can entangle a pair of gravitons (which are only theoretical, but who knows for sure?) and separate them over a vast distance. Hold on - ...
0
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0answers
18 views

Energy transfer (Bohr's stopping formula vs. Bethe's)

I'm currently reading about Bohr and Bethe stopping, and has come across a thing I can't entirely figure out. In my book it states: "Bohr's formula gives a reasonable description of the energy loss ...
3
votes
2answers
90 views

Do photons with a frequency of less than 1 Hz exist?

A photon with a frequency of less than 1 Hz would have an energy below $$ E = h*v < 6.626×10^{−34} J $$ which would be less than the value of Planck's constant. Do photons with such a low energy ...
1
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2answers
104 views

Unitary operator algebra and multiplying by identity

If $\hat{H}$ is Hermitian, with eigenvalues $a_k$, then $$\hat{H} = \sum_k a_k \left|\psi_k\right> \left<\psi_k\right|.$$ I read that it then follows that $$\begin{align*} e^{i\hat{H}} = ...
3
votes
1answer
49 views

Most general separable solution of free Dirac equation

In relativistic quantum mechanics, the solution of the free Dirac equation is assumed to be $$\Psi(\textbf{r},t)=u(\textbf{p})e^{i(\textbf{p}\cdot \textbf{r}-Et)}$$ How do I know that this is the most ...
0
votes
1answer
45 views

Definition of a “variable” in a Hamiltonian? [closed]

What does this mean $c^+c$ when included in a Hamiltonian? I saw it in a Hamiltonian with Sigma Notation and I want to know what it means. Or is its definition specific to the given Hamiltonian?
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0answers
27 views

Eigenstates of operators on constituent systems in tensor product space

Suppose I have two entangled physical systems $\mathcal{A}$ and $\mathcal{B}$ with respective hilbert spaces $\mathcal{H}_{\mathcal{A}}$ and $\mathcal{H}_{\mathcal{B}}$. If $A,B$ are operators on ...
-4
votes
2answers
204 views

Faster than light signals and the price to be paid if we accept them : a very simple protocol

Most physicists currently understand entanglement as transferring information instantaneously, yet not violating causality. Is this really a satisfactory explanation, or should be look for something ...
0
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1answer
21 views

Distinguishing between prepared and unprepared states Stern-Gerlach experiment

$ \newcommand{\bra}[1]{\left\langle #1 \right|} \newcommand{\ket}[1]{\left| #1 \right\rangle} \newcommand{\braket}[2]{\left\langle #1 \middle| #2 \right\rangle}$I have a problem and am confused as to ...
0
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3answers
75 views

Can only one electron or photon produce interference pattern?

If we shoot one electron or photon at a time to a double slit for a long time, interference pattern will build up on the other side. If the gap between each electron or photon is long enough that they ...
0
votes
3answers
116 views

Justifying the notation $\langle x\ |\ \psi\rangle$ [duplicate]

I came across this expression: $$\langle x\ |\ \psi\rangle=\psi(x)$$ How can it be justified? I understand the LHS as an inner product, and the RHS just as a function of the parameter $x$.
0
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2answers
76 views

Why uncertainty principle on a large scale doesn't impose limitations on precision?

The question is By choosing reasonable numerical values for mass and velocity, show that $\Delta x \Delta p >=\frac{ \hbar}{2}$ doesn't impose any limitations on the precision with which the ...
0
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0answers
12 views

relation between chemically activity and work function and fermi level

I am trying to connect the following concepts together : "being chemically active", "work function" and "fermi level" I want to know if for a metal, "being chemically active" is equivalent to "its ...
3
votes
3answers
94 views

Applying rotation operator to spin

I would like to fully understand all the steps in the algebra when applying a rotation operator to a spin state. Suppose we have the spin state: $|\Psi(0)\rangle=c_+|+\rangle+c_-|-\rangle$ for a ...
0
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0answers
25 views

Degenerate perturbation theory for n=3 hydrogen

I just studied Zeeman effect for $n=2$ hydrogen and am trying to extrapolate it to $n=3$. However, I am unable to understand how to get the perturbation matrix (and express it in block-diagonal form) ...
4
votes
1answer
253 views

Numerical solution to Schrödinger equation - eigenvalues

This is my first question on here. I'm trying to numerically solve the Schrödinger equation for the Woods-Saxon Potential and find the energy eigenvalues and eigenfunctions but I am confused about how ...