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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157 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 ...
1
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0answers
75 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
164 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 ...
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1answer
102 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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1answer
55 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
296 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 ...
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1answer
58 views

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

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
113 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 ...
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0answers
32 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 ...
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0answers
47 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
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2answers
292 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
168 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 ...
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1answer
106 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
43 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 ...
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0answers
168 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 ...
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1answer
55 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 ...
2
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1answer
520 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 ...
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1answer
511 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 ...
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4answers
92 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 ...
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3answers
583 views

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

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 ...
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1answer
140 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 ...
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1answer
127 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
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1answer
670 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 ...
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2answers
56 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
99 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 ...
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0answers
47 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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5answers
366 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} ...
3
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1answer
129 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
218 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 - ...
3
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2answers
233 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
175 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}} = ...
4
votes
1answer
144 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 ...
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0answers
52 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 ...
2
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3answers
637 views

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

Some physicists currently understand entanglement as transferring information instantaneously, yet not violating causality. Is this really a satisfactory explanation, or should be look for something ...
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1answer
116 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 ...
2
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4answers
946 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 ...
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3answers
153 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 $x$.
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2answers
151 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 ...
3
votes
3answers
163 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 ...
4
votes
2answers
3k 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 ...
0
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2answers
583 views

Please explain the following graphs that describe a quantum mechanical harmonic oscillator

Graphs such as the above keep coming up when talking about harmonic oscillators in a quantum mechanical sense. However, I simply cannot make sense of them. What does each line represent why are they ...
2
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0answers
82 views

Why does this 'Quantum Pinned' superconductor allow easy repositioning

I'm confused by videos such as this (popular demonstration of 'Quantum Levitation'): https://www.youtube.com/watch?v=Ws6AAhTw7RA So my current understanding of superconductors is that when in the ...
1
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0answers
54 views

In Grover and Shor Algorithms 2 registers of qubits are handled at books, but it's really just one seen as 2?

I found in the literature that we require at least two quantum registers for arithmetics operation. Example: The function $f(x)=x^2$ is then a unitary evolution of the two registers, in this ...
4
votes
3answers
308 views

Are the authors saying that the observer effect plays no role in Bohr's thought experiment of the Heisenberg uncertainty principle?

Here is an excerpt from Eisberg & Resnick's Quantum Physics of Atoms, Molecules, Solids, Nuclei, and Particles. Here is introducing Bohr's though experiment to establish a physical origin for the ...
3
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1answer
174 views

Are Forces Involved Non-Local?

Below is a copy of a answer given to this Phys.SE question asked previously: Does every material thing just consist in forces? In short, assume that we have two labs A and B, in each one there is ...
1
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1answer
78 views

Timing of photon emission by electron in bound state

A photon is emitted by an electron (which is in a bound state). Is the energy of the electron lost immediately, or is the energy emitted during the complete transition time? I think my second ...
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1answer
99 views

In what ways does matter behave like a wave? [duplicate]

thanks in advance for the help. Mainly, what characteristic of matter is wavelike? Does is physically move up and down like a wave, does it phase in and out of existence with a wavelike gradient, or ...
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0answers
36 views

What kind of potential profile that an electron live in provides bound state energy levels?

Given the electron Hamiltonian $$H=T+V(r)$$ where $T$ is the kinetic energy, $V$ is the potential energy and it is not necessarily isotropic. If $$V \sim -\frac1{|r|},$$ we have hydrogen-like bound ...
3
votes
3answers
419 views

Why does the electron spin with a particular tilt?

I found this image for the classical description of the electron spin at hyperphysics Can you explain why the axis of rotation makes an angle of 60° with the z-axis and how this particular ...
5
votes
3answers
1k views

What is the difference between maximally entangled and maximally mixed states?

To my understanding, mixed states is composed of various states with their corresponding probabilities, but what is the actual difference between maximally mixed states and maximally entangled states? ...