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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16 views

Angular Momentum Expectation Values in Spherical Coordinates

I have a homework problem that asks: Using the spherical harmonics calculate $\langle J_x \rangle$, $\langle J_y \rangle$, $\langle J_z \rangle$ in the state $|l,m\rangle$. Use the derivative forms ...
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14 views

Compatible Observes and Measurement

Suppose $A$ and $B$ are compatible observes (i.e. $[A,B] = 0$). We take the eigenkets of $A$ to be $|a_1 \rangle \ldots |a_N \rangle$. Further, we suppose that the first $k$ eignekets of $A$ are ...
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2answers
48 views

Transition from 4-potential to E and B

In my lecture notes there is a step that i cannot follow: $$\frac{i}{2}[\gamma^{\mu},\gamma^{\nu}] (\partial_{\mu}A_{\nu}-\partial_{\nu}A_{\mu})=: \sigma^{\mu\nu}F_{\mu\nu}=i\vec{\alpha} ...
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0answers
13 views

why does the spaceship stand still in the bubble while movement is taking place outside? [on hold]

The question concerns travel faster then the speed of light.Another quesion conecerning the colour in the front being bler och the colour in back being redder. How it possible just these two colours ...
2
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1answer
48 views

Time Evolution of Position Operator

I am trying to understand why $$e^{-it\triangle}xe^{it\triangle}=x-2it\nabla$$ where $x$ is just multiplication operator by $x$. In particular, the text says this can be seen by differentiating with ...
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14 views

What is the reason for 2 qubits no longer being entangled after interaction with a causality violating qubit?

Background : I was reading the following paper on closed timelike curves ( CTC ) : Quantum Mechanics Near Closed Timelike Curves. The Deutsch consistency equation for CTC is $$\rho_{CTC}=Tr_{CR}( U ...
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22 views

p-adic and quantum mechanics [duplicate]

In physics we call integer based quantity as “quantization”, so you have energy, momentum etc taking quantized values. But in math, this kind of situation is really the age old problem of number ...
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1answer
33 views

Derivation of Pauli Hamiltonian

In my lecture notes there is a step that i cannot follow: $$\frac{i}{2}\epsilon_{ijk}\sigma_k [\pi_i,\pi_j] = -e\epsilon_{ijk}\partial_iA_j\sigma_k$$ with $\vec{\pi}=\vec{p}-e\vec{A}(x)$ When I ...
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1answer
32 views

What are the units of the creation and annihilation operators?

The creation and annihilation operators - also known as ladder operators are; $ \hat{a}^\dagger$ and $\hat{a}$ respectively. Using the equation $\hat{H} = \hbarω\left(\hat{a}^\dagger \hat{a} + ...
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2answers
166 views

What exactly implies the need of quantum mechanics for self-adjoint and not only symmetric operators? [duplicate]

We know that quantum mechanics requires self-adjoint operators, not only symmetric. Can we say that this follows ONLY from the two following axioms of quantum mechanics, namely that each observable ...
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19 views

Is quantum superposition an actual, physical phenomenon? [duplicate]

Correct me if I'm wrong, but I'm given to understand that the intention of Shrodinger's thought experiment was to point out the folly of the Copenhagen interpretation, in that a quantum particle being ...
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0answers
29 views

Ladder Operator proof

I was wondering what the proof was that a ladder operator will generate all the eigenenergies for a system. e.g. the QM harmonic oscillator. So after manipulating the ladder operator we get; ($a$ is ...
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0answers
25 views

joint probability distribution in QM

The problem of incompatible observables in quantum mechanics is often explained in terms of their (self-adjoint) operators having different sets of eigenstates. This causes their commutator to be ...
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1answer
37 views

Recurrence differential equations

We all know recurrence equations like e.q. Fibonacci relation $$F_{n} = F_{n-1} + F_{n+1}$$ In order to find general expression for any $n$, we can use generating function method $$G(x) = ...
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0answers
15 views

Can any experiments NOT be done through the classic control-experimental groups method? [on hold]

The classic control-experimental groups method involves having a control group to measure what happens when everything is regulated, and then one or more experimental groups are used, each having one ...
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1answer
84 views

Quantum violation of Newton's Third Law? [on hold]

From this site: http://www.learning-mind.com/5-thought-provoking-quantum-experiments-showing-that-reality-is-an-illusion/ I gained the knowledge that a group of scientists, upon measuring a tiny ...
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0answers
13 views

Quantum dual-slit experiment via Youtube live streaming (explanation within)?

What will happen with this theoretical setup: A scientist is bored one day and positions his photon detector at the classic dual-slit photon experimental setup. Then he wires the photon detector up to ...
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3answers
143 views

Deriving cross product from angular momentum algebra

Is it possible to derive: \begin{equation} \hat{L}=\hat{r}\times \hat{p} \end{equation} from the angular momentum algebra: \begin{equation} [\hat{L}_i,\hat{L}_j]=i\ \hbar\ \epsilon_{ijk}\hat{L}_k\ ? ...
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41 views

Density matrix in Quantum Statistical Mechanics

What is the connection between the density matrix in quantum statistical mechanics and the probability of being a particular state in classical statistical mechanics? It would seem that the elements ...
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1answer
45 views

BB84 protocol what do they do once they have the key?

In the BB84 protocol Alice and Bob share a key via a method using both quantum and classical channels. I understand how they do this. But I don't understand what they then do with the key? I.e. How do ...
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1answer
33 views

Calculation & derivation of de-Broglie wavelength [duplicate]

How to calculate the de Broglie wavelength of an $\alpha$ particle that is accelerated through a potential difference of $V$ from rest.
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4answers
571 views

Can dimension analysis be used in developing more advanced physics equations?

It is obvious that dimensional analysis can be used to derive many classical mechanics equations (excluding constants). As long as all the dependent quantities are known. My question is whether this ...
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36 views

Solutions to Dirac equation in 2+1 D [on hold]

Hello I solved the Dirac equation in 2+1 D taking two different gamma matrix representations. rep.A: $$\gamma^0=\sigma^3, \qquad\gamma^1=i\sigma^1, \qquad\gamma^2=i\sigma^2.$$ rep.B: ...
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23 views

How do I know the limit for the calculation of normalized wave function.

Let we have a eigen function for dumbbell ball given which is $ \phi= A e^{i x}$ and I have to determine the normalization constant A. I know in thios case I will have to write $$\int \phi \phi^* ...
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2answers
38 views

Why does the raising operator, when acting on a ket with a maximum second quantum number, yield zero?

I'm studying the general formalism of angular momentum in quantum mechanics from Zettili's "Quantum Mechanics: Concepts and Applications", and came across the following equation (labeled 5.37) on page ...
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2answers
77 views

Perturbation theory in quantum harmonic oscillator [on hold]

This question concerns the quantum harmonic oscillator: (a)Express the operator $\hat B = \hat x \hat p + \hat p \hat x + \hbar$ in terms of $\hat a_{\pm}$ and $\hbar$ (b)Write the matrix ...
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1answer
12 views

Do electric sinusidal waves rotate 45 degrees too when light pass through a hollow cylindrical magnet or just the sinusoidal magnetic waves do that?

Do electric sinusoidal waves rotate 45 degrees too when light pass through a hollow cylindrical magnet or just the sinusoidal magnetic waves do that?
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1answer
41 views

Orbital angular momentum of electrons

In a QM class, to study the hydrogen atom, we started by defining the Hamiltonian $H$ for a central potential, then made an orbital angular momentum operator appear as part of $H$, then down the line ...
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0answers
26 views

Blackbody cavity relationship between energy of oscillators and EM radiation?

This question is based on Planck's view of blackbody radiation in a cavity. Here is a quote from here: ...where $< E >$ is the average energy of the oscillators present on the walls of the ...
5
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1answer
572 views

What does it mean for a particle to have spin of 2? [duplicate]

When I first started to study quantum mechanics, my physics text book told that particles have spin of either 1/2 or -1/2. Then I recently read an article saying that gravitons are expected to be ...
1
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1answer
26 views

Confusion about Shankar 1D Scattering in a Single-Step Potential

Section 5.4 of Shankar studies the problem of a single-step potential where $$V(x) = \begin{cases}0&x<0\\V_0 &x>0\end{cases}.$$ It was shown that a incident Gaussian packet $$\psi_I(x,0) ...
2
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1answer
55 views

Ehrenfest's Theorem “contradiction”?

Ehrenfest tells us that for $\hat{p}$ $$\partial_t \langle p \rangle = \langle -\partial_x V \rangle$$ I also understand the basic steps in deriving this result directly by taking the time ...
2
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1answer
42 views

Planck's postulate for oscillators or for light?

I know that Planck originally postulated that the energy of an oscillator in a black body was quantised to $E=nh\nu$ but did he know at the time that this meant the energy of light was also quantised ...
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0answers
19 views

Ground State energy as a function of $N$ and $B$, $E_0(N,B)$

The one-particle Hamiltonian is given by: $$\hat{H}=\frac{1}{2m}\left(p+\frac{e}{c}A\right)^2$$ where $p=\hbar\vec{k}$ with $e > 0$ and vector potential $A=(0,x,0)B$, such $B=\triangledown ...
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0answers
31 views

Total Hamiltonian of a system of two particles

In my QM class, we talked about the total Hamiltonian of a system of two spin $1/2$ particles: \begin{equation} H^T=H_1\otimes\mathbb{1}+\mathbb{1}\otimes H_2. \end{equation} It was suggested that ...
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2answers
12 views

Enforcing the exchange criteria for two particles in a box in different states

Suppose you have two identical particles (for simplicity we can think of spin 0 bosons for which are represented as a scalar wave-functions, but fermions have a similar problem) in a 1D box that ...
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0answers
27 views

What is the equation for the pressure at which neutrons can no longer be supported by neutron degeneracy pressure?

What is the equation for the pressure at which neutrons can no longer be supported by neutron degeneracy pressure? At which point they would collapse into each other. There seems to be one for ...
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0answers
24 views

An analogy for qubits and quantum computing?

I have understood that qubits are special ways to store data where they exist in more than the conventional 2 states. However, I do not understand how they are read, interpreted and manipulated ...
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24 views

Polarisation states in 1d?

I am working through a derivation of the spectral energy density in a 1d cavity. The derivation says that the number of modes (per unit volume) in a frequency interval $dv$ is given by: $$g(\nu)d\nu ...
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1answer
39 views

What causes a wavefunction to move? [on hold]

I understand that a wavefunction evolves with time. The explanation, that I got from the book is that this is due to changing regions of constructive and destructive interference. What then, causes ...
2
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1answer
61 views

What is the meaning of commuting Hamiltonians?

I have two quantum mechanical Hamiltonians such that \begin{equation} [\hat{H}_1,\hat{H}_2] = 0, \end{equation} where $\hat{H}_1$ and $\hat{H}_2$ act on the same set of states. What is there to ...
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0answers
18 views

SUSY without gaugino [on hold]

In Minimal Supersymmetric Standard Model (MSSM) with $R$-parity, gauginos have Majorana mass. If we use $R$-symmetry instead of $R$-parity, gauginos do not have Majorana mass. But they can acquire ...
2
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3answers
392 views

How do particles “know” when to decay?

So, as I understand it, in a substance that is made of radioactive elements, the half-life tells us how long until the half of those atoms decay into their next atom [is there a name for that: the ...
2
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2answers
102 views

Tensor product of operators in QM

If I wanted to find the coefficients of a linear transformation between 2 vectors in the basis for 2 spin $1/2$ paticles (let's say for starters we are not even looking for a unitary transform): ...
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1answer
41 views

Applying Schrodinger equation to find the energies of a free electron model in a metal [on hold]

The one-particle Hamiltonian is given by $$\hat{H}=\frac{1}{2m}\left(p+\frac{e}{c}A\right)$$ with $e > 0$ and vector potential $A=(0,x,0)B$, such $B=\triangledown \times A=(0,0,B)$ Question: "I ...
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2answers
33 views

Probability Amplitude AA* source?

I was watching a video about fundamental Quantum Mechanics. The video lecture is excellent but I am confused after hearing the part at the 9.46 sec of this video . He said repeatedly from the ...
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45 views

Interpretations of Quantum Mechanics and Locality

I have read these posts here: Why do people still talk about bohmian mechanics/hidden variables Disproof of Bell’s Theorem What combinations of realism, non-locality, and contextuality are ruled ...
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14 views

How to count total spin degeneracies for many spin one half particles?

Given the spin operator for particle $j$ \begin{align} \bar{S}_{j} = \left( \bigotimes_{k=1}^{j-1} I_{k} \right) \otimes \left(\tfrac{\hbar}{2}\bar{\sigma}\right)_{j} \otimes \left( ...
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2answers
62 views

Atomic orbitals

I just studied atomic orbitals in a theoretical QM class, and I'm left with several questions, that are probably more questions in quantum chemistry: Many orbitals seem to have a preferred axis - ...
5
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1answer
56 views

Understanding electronic band structure diagrams

Currently I'm trying to understand electronic band structures such as depicted below: And following questions were arisen. Why are there multiple lines in valence side and conduction side? Where ...