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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128 views

Number of distinct Feynman Diagrams for different orders of $\phi^4$ theory for 2 point function

There is 1 distinct Feynman diagram for zeroth order and 2 distinct diagrams for first order in $\phi^4$ theory for two point function. I want to know is there a way to predict the number of distinct ...
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53 views

Measure-theoretic maths behind Born's probabilistic interpretation of Schrodinger's equation

I was reading a bit about Quantum Mechanics, Schrodinger's equation and its probabilistic interpretation (found this very insightful intro here https://plus.maths.org/content/schrodinger-1), my ...
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38 views

Landau levels in ferromagnets

Consider a spontaneously magnetised (uniformly) conducting ferromagnet. Now suppose that there is no external magnetic field. The question is as follows: will the motion of electrons be quantized via ...
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72 views

Determine the number of bound states admitted in Schrodinger system

Is there a general method for determining the number of bound states admitted by a potential in the Schrodinger equation? Certainly the number of dimensions must factor in somehow: the delta ...
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51 views

Condition for CP violation

I am studying how weak and strong phases lead to CP violation. I am following CP Violation by Branco. There is some algebra that I can not follow. Consider the process : $ a + \bar{a} \rightarrow b ...
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63 views

Is there a video of a double-slit experiment using walking oil droplets (aka dotwaves)?

I've heard there have been experiments with walking droplets in a double-slit setup, and I've seen videos of many of the other quantum phenomenons walking droplets can emulate, but I can't find one of ...
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34 views

why are quantum vortices so large?

Quantum vortices in helium are almost macroscopic, and can be be imaged in a light microscope: http://www.aps.org/units/dfd/pressroom/papers/gaff09.cfm How can vorticity be quantized on such a large ...
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54 views

Ordering of eigenstates in the quantum adiabatic theorem

Suppose we have an 'initial' Hamiltonian $H_{i}$ whose eigenvalues are all non-degenerate, which we order as follows: $ E^{0}_{i} < E^{1}_{i} < \dots < E^{N-2}_{i} < E^{N-1}_{i}$ Suppose ...
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85 views

Why is the activation energy of combustion so large compared with regular bonding?

I wanted to know why combustion requires an activation energy and I found this article (see this too). It says that molecular oxygen ground state is a triplet state (according to Hund's rules), and ...
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69 views

What's actually going on when light interacts with matter?

There are many different theories but all of them fail to explain all 3 phenomena of light(absorption,emission,transmission). https://www.youtube.com/watch?v=CiHN0ZWE5bk ...
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53 views

Conservation of momentum in Heisenberg's microscope

In working through Heisenberg's microscope, conservation of momentum for the photon and electron tells us that \begin{align} \frac{h}{\lambda}=\frac{h}{\lambda'}\sin\theta+p_x\,, \end{align} where ...
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75 views

Amplitude for a string to propagate from one point to another

In Zwiebach’s book sections 12.6 and 12.7 interesting aspects of the wave function of the string are discussed. In order to introduce my question first recall what happens with the relativistic ...
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58 views

Maximizing particle annihilation of a certain particle type?

Is there any theoretical situation where one would be able to maximize the production of a certain type of particle? I wish to continue discussing this question: Where would dark matter be produced? ...
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141 views

Weak measurement and weak value

The concept of weak measurements (and weak values) have become popular in Quantum information community, as I can see quite a few papers in arXiv. Since I am from Mathematical background (and the ...
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98 views

About the definition of the spin current

People have been talking about the spin current for a while. But there is a fundamental problem. Unlike charge, or mass, spin is not conserved. Let us take the 1d spin-1/2 Heisenberg chain as an ...
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85 views

Why do we need to suppose the chemical potential is zero in this situation?

I've been working on some statistical mechanics problems and one of them asks to compute the pressure with chemical potential zero of a boson gas whose particles do not interact and whose energies are ...
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57 views

Interpretation of the diode constant in a LED

For a real diode the current as function of the potential difference between its terminals (for big enough voltage) is given by: $$I=A e^{\frac{eV-E}{\eta k_B T}} \tag{1}$$ So in the case of LEDs ...
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75 views

Non-Linear O.D.E

I have reached a set of ODE as \begin{align} &\ddot{\vec{a}}(t)+\omega_0^2\frac{\cos{(b(t))}\sin{(a(t))}}{a(t)}\vec{a}(t)=0\\ &\ddot{b}(t)+\omega_0^2\cos{(a(t))}\sin{(b(t))}=0 \end{align} ...
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34 views

Current density defined by the scattering operator

I have a problem with the definition of the current density. In most literature it is defined as $j^\mu=\frac{i}{2}(S^*\frac{\partial S(A)}{\partial A_\mu(x)})$. I understand that normally we use ...
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62 views

Ground state symmetry breaking in Bose-Hubbard model with spin-orbit coupling

The Hamiltonian for 2D Bose-Hubbard model with spin-orbit coupling on a square lattice is written as $ H = -t\sum_{\langle ij \rangle}\Psi_i^{\dagger}\Psi_j^{\vphantom{\dagger}} + ...
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34 views

How asymptotically efficient is quantum state tomography of a flat qubit?

Suppose you receive $n$ copies of a qubit rotated by an unknown angle. That is to say, you're given the state: $$T(\theta) = \left(\sin(\theta) \left|0\right\rangle + \cos(\theta) ...
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162 views

Ghost in the quantization of relativistic particle

It is well known that in the quantization of certain relativistic theories such electromagnetism or relativistic string negative norm states could arise when quantizing covariantly. Acting with ...
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21 views

Does the trial index of typical CHSH experiments constitute a “hidden variable”?

In typical experiments related to the CHSH inequality there are individual detections being made by two separate (analyzer-and-)detector systems, "System $A$: $(D_A^+, D_A^-)$" and "System $B$: ...
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66 views

Understanding quantum coherence in biological processes (Magnetoreception)

Moved my questions to the top. Context below. Why is the strength of the electric field and the coupling constant being compared to the inverse coherence time? What is the inverse coherence time? Is ...
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52 views

Second-order correction in Quantum-Confined Stark effect

In the wikipedia article, there is a second-order correction in the Quantum-Confined Stark Effect. I could not understand how it was solved. I did not understand the meaning of 2(0) and 1(0) and how I ...
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141 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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56 views

How does a Bell measurement physically look like?

I do know how Bell states look like. They can be distinguished by doing a Bell measurement. A measurement has 4 possible outcomes (as there are 4 states, which form orthonormal basis). However I have ...
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58 views

Why is the water diamagnetic?

I checked using my permanent magnet that water is diamagnetic. But why is it like that? Does this have any important consequence for life?
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81 views

Geometric measure of entanglement for fermions or bosons?

For a system consisting of multiple components, say, a spin chain consisting of $N\geq 3 $ spins, people sometimes use the so-called geometric measure of entanglement. It is related to the inner ...
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216 views

Degeneracy of Rotational Energy Levels of a Diatomic Molecule

To derive the energy levels of a diatomic molecule (with the z axis the axis of symmetry of the molecule), we write the Hamiltonian as ...
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45 views

What physical effects cause materialization of a system of particles for a short time?

It is well-known from physics that a photon with enough energy creates a pair of particles: one electron and one positron. This pair of particles can only exist for a short time. This process is ...
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81 views

commutation relations for operators in projected subspaces

I am looking for a consistent re-definition of commutators for certain operators when I work in a projected subspace. Basically, I have a spin defined in terms of 4 Majorana operators $b_{x}$, ...
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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 ...
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146 views

Double slit experiment in the Heisenberg picture

In the Schrödinger picture the wave function evolves and the observables stay constant. In that picture it's not too hard to imagine how does the wave function spreads interferes and diffracts, and ...
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78 views

Relation between representations/classifications

Generally a quantum system can be characterized in the following way: its states form a representation space for every symmetry group of that system. The representation has to be unitary (or ...
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205 views

What is the symmetry group of this Hamiltonian?

Consider a Hamiltonian $$\hat H=-\partial_x^2-\partial_y^2+(x-y)Q,$$ where $x,y\in[0,a]$ (homogeneous Dirichlet boundary conditions assumed), and $Q$ is some real parameter. When $Q=0$, the ...
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44 views

Ground state energy in a simple quantum gravity situation

I found this problem in an MIT undergrad QM problem set; it is problem number 2, part a, number iv. I'll summarize everything below, but here's the link: ...
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294 views

Majorana zero mode and 1D Ising model

It is known that the one-dimensional (1D) Ising model can be mapped to a free Majorana model using a Jordan-Wigner transformation and its two degenerated ground states are well interpreted by the two ...
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39 views

Simplification of matrix-element given the Wigner-Eckardt theorem and Clebsch-Gordon coefficients of a 1,1/2 system

How can I simplify the following matrix-elements $$\left\langle 1,1/2;m_1,m_2\left| S \right| 1,1/2;m_1^{'},m_2^{'} \right\rangle$$ given the Wigner-Eckard theorem $$\left\langle j,m|S|j^{'},m^{'} ...
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207 views

Is it possible extend Schrodinger theory in relativistic contexts with naive consideration?

Preamble Let's consider a generic sinusoidal wave $\Psi (\mathbf{r},t) = A e^{i(\mathbf{k} \cdot \mathbf{r} - \omega t + \phi)}$ and let's insert it into Schroedinger equation (please note that $ ...
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102 views

Is time depending on the observer in string theory?

I heard that in the theory of relativity the time of an action is depending on the observer. But in string theory, is the time also depending on the observer? Are strings acting according to the ...
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156 views

A problem with the Gamow state

Consider a form of potential $U(r)$ as follows $$ U(r)=\begin{cases}0 & 0<r\leq a \\ U_0 & a<r\leq b \\ 0 &r>b\end{cases} $$ In this problem $r$ is the distance from the origin, ...
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79 views

Why does the time-independent perturbation theory become no longer useful when its order gets larger?

In Griffith's Introduction to Quantum Mechanics p. 256, after figuring out $$E_n^2=\sum_{m\neq n} \frac{|\langle\psi_m^0|H'|\psi_n^0\rangle|^2}{E_n^0-E_m^0}$$ he says We could go on to calculate ...
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95 views

Physical interpretation of a certain Hamiltonian

Consider a $2 \times 2$ Hermitian (or symmetric) matrix-valued function $$g(x) = \{ g_{jk}(x)\}_{j,k=1,2}, \quad x \in \mathbb{R}^{2},$$ such that $0 < m_{-}I \leq g(x) \leq m_{+}I$, for some ...
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58 views

Estimate of the second shallowest bound state?

Suppose we have a 1D potential $V(x)$ of finite range, i.e., $$ V(x) ~=~0 $$ for $|x| > b $. The potential is assume to support at least two bound states, but might have more, say $n\geq 2$. ...
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2k views

Cohen Tannoudji solutions to exercises

Does anyone know where to find the solutions to the exercises of Cohen-Tannoudji's Quantum Mechanics? I am gonna try to do all of them and would like to check.
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66 views

Making An Energy Momentum Plot For A Rashba Model (Using Discretization)

I want to make a plot of the Energy versus the Momentum of the Rashba model, using discrete matrices. First Ill show how I did this for the free particle. Subsequently I will show what goes wrong for ...
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82 views

Do coupled angular momentum eigenstates depend on angle between particle positions?

Suppose we have two particles with positions $\vec r_1$ and $\vec r_2$. The corresponding coupled angular momentum eigenstates would be expressed via Clebsch-Gordan coefficients as (according to this ...
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56 views

Rationale for definition of input/output operators in quantum langevin equations

I am going through Gardiner & Zoller's 'Quantum Noise', and following the derivation of the Langevin equations in terms of input/output operators. Let the bath Hamiltonian be: ...
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96 views

Statistics of many body systems in pure states

My understanding of describing a system in thermal equilibrium is that we introduce an ideal thermal reservoir for convenience and then imagine that the system+reservoir samples all states of constant ...