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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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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42 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
187 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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35 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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36 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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45 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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1answer
98 views

Quantum violation of Newton's Third Law? [closed]

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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23 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
164 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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56 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
52 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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43 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
683 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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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
42 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
100 views

Perturbation theory in quantum harmonic oscillator [closed]

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
13 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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53 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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1answer
108 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 $\langle E \rangle$ is the average energy of the oscillators present on the walls of ...
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1answer
597 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 ...
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1answer
56 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 ...
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1answer
47 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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21 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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2answers
16 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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36 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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26 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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25 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 ...
2
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1answer
75 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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3answers
413 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 ...
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2answers
118 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
46 views

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

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
36 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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47 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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15 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
70 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 - ...
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1answer
83 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 ...
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0answers
30 views

Intuition behind modeling quantum impurities as two-level systems

I've been trying to get a basic understanding of quantum impurity problems, starting with the Anderson model. The Wikipedia article (along with some review articles) seems to explain the simplest ...
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1answer
37 views

How to determine if a potential admits bound states?

According to Griffith's Quantum Mechanics, "$E$ must exceed the minimum value of $V(x)$, for every normalizable solution to the time independent Schroedinger equation" As an example, there is no ...
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2answers
59 views

What is the implication of Schmit decomposition?

According to schmidt decomposition if I have pure state $|\psi\rangle$ in the composite hilbert space $AB$ ( both $A$ and $B$ are hilbert spaces of dimension $n$ ) then it can be writen as ...
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40 views

Time evolution of interaction Hamiltonian in the Heisenberg picture

How does the interaction Hamiltonian of a (finite dim) quantum system with Hamiltonian: $H(t) = H_0 + w(t) H_I$ evolve in time in the Heisenberg picture. Is there anything special about the way ...
4
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1answer
49 views

Do 2-body elliptic orbits precess in special relativity?

Einstein famously explained the anomalous precession of Mercury by showing that in general relativity elliptic orbits precess even in the 2-body problem. But apparently in the early days of quantum ...
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1answer
23 views

Scintillation from wave function

Suppose we have a system with a (non-relativistic) electron whose state is described by a time-dependent wave function $\psi(x,t)$. Then I think it's correct to say that if we introduce a phosphor ...
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1answer
34 views

Question about group velocity and travelling waves

I'm trying to learn some basic quantum mechanics and I have a question related to group velocity of a travelling wave. I know there are already a few questions related to group velocity, but I ...
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1answer
80 views

How to show time reversal symmetry does not break in the tight binding Hamiltonian for the honeycomb lattice?

The Hamiltonian of the honeycomb lattice is $$ H=\sum_{k\sigma}t(k) a_{k\sigma}^\dagger b_{k\sigma}+h.c $$ Where $t(-k)=t^*(k)$. If we do a time reversal transformation(according the answer to this ...
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1answer
105 views

What is the idea behind canonical quantization?

From what I understand, canonical quantization of a classical theory consists of replacing the observables by abstract operators, of which only the commutation rules, which have to correspond to the ...
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0answers
56 views

The wavefunction of the superconductor A consists of two parts: B and C

In reading this article, I come across this paragraph: The pink marked place is where I can't understand, why can we use direct product of the former but not the later? This is may be a basic ...
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1answer
73 views

Path dependent phase in quantum mechanics

In elementary treatments of quantum mechanics, we are taught that the wavefunction of a single particle is complex valued ($\Psi : \mathbb{R}^3 \to \mathbb{C}$). In particular, the wavefunction has a ...
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14 views

Metastable bound state in resonance scattering

In resonance scattering, why does the mean lifetime of the "metastable" bound state depend inversely on the width of the resonance?
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2answers
46 views

Spin State Energy Levels

When a spin-1/2 particle is placed in a magnetic field that is strong enough and varies slowly enough in space and time, it will become polarized and its spin will either align or anti-align with the ...
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2answers
86 views

“Equidistant” spectra in quantum mechanics [duplicate]

In one-dimensional quantum mechanics, it seems that the only kind of potential able to produce an "equidistant" spectrum, i.e. with $E_{n+1}-E_{n}=\text{constant}$, is the harmonic oscillator. Why is ...