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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Weak Anti-Localization

On Wikipedia (pretty much the only place I can find an explanation of what weak anti-localization actually is) it is explained as: In a system with spin-orbit coupling the spin of a carrier is ...
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356 views

How to express continuous values as a matrix

Usually a quantity of a matrix is defined as the eigenvalues of the matrix. If so, how can anyone express continuous values, as in Schrodinger picture, into a matrix?
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195 views

If $L$ is a matrix that represents real physical quantity, why is $L^2$ non-negative real physical quantity?

In my textbook, it says that when $L$ is a matrix that represents real($\mathbb{R}$) physical quantity, $L^2$ represents non-negative real physical quantity. What would be the proof of this?
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237 views

Commutability of two physical quantity matrices

Suppose that two matrices $A$ and $B$, representing real($\mathbb{R}$) physical quantity, can be multiplied commutatively with each other; i.e. $AB =BA$. However, each matrix cannot be multiplied ...
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Is the minimum radius of a positronium system of the order of compton wavelength or less than that?

Since from electron-positron annihilation energy and uncertainty principle,the minimum radius of positronium comes out as half of the compton radius.
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Energy is quantized

How can energy be quantized if we can have energy be measured like in 1.56364, 5.7535, 6423.654 kilo joules, with decimals? Thanks Also isnt it quantization means energy is represented in bit ...
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Proof of Yang's theorem

Yang's theorem states that a massive spin-1 particle cannot decay into a pair of identical massless spin-1 particles. The proof starts by going to the rest frame of the decaying particle, and relies ...
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385 views

What is crystal field anisotropy or effect ? It forces the magnetic moment to point in particular local direction..

Can you give a basic explanation of what is crystal field anisotropy ? What is the reason to arise ? In spin ice it forces the dipoles to point in the local 111 direction. For partially filled rare ...
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82 views

How Lyman transition (to the ground state from higher excited) happens ? The dipole selection rule is +/- 1?

How are the lyman series observed when the dipole selection rule is +/-1 in l change for hydrogen atom ?
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117 views

How is explained the lower ionization potential for atoms compared to closed shell nobel atoms?

Why adding just one electron changes tremendously the ionization potential from any of the nobel atoms ? If it is the screening why adding a second electron increases the ionization potential ? ...
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Why 2s state is lower in energy that 2p state in atoms?

The s orbital have higher probability to be closer to the core and feels larger attraction than the p orbital and on average is further away and in addition p has repulsive potentilal l(l+1)h^2/2mr^2. ...
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79 views

A physical quantity that is a real combination and commutability

Suppose that a matrix $$A ~=~ x_1 B + x_2 C$$ is a linear combination of two self-adjoint matrices $B$ and $C$. I'm interested in when $A$ represents a physical quantity. When the linear ...
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200 views

Matrix representing the quantity - why can some matrices not be physical quantity?

In Heisenberg picture, my textbook says that the following matrix $A = \frac{5}{3}\Sigma_1 + i\frac{4}{3}\Sigma_2$ cannot represent physical quantity. the book says this is because ...
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997 views

Does a microwave resonantly excite the rotational levels when cooking?

Wikipedia states there is no resonance absorption, but says at the same time that the molecules are oscillating like dipoles, which is kind of the same if you are exciting the rotational levels ? The ...
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260 views

Normalization of a spin-like quantity in matrix mechanics

Suppose that there is a quantity in Heisenberg picture as the following: $A=u_1\Sigma_1 + u_2\Sigma_2 +u_3\Sigma_3$ I am not sure why $u_1,u_2,u_3$ is normalized to be ${u_1}^2 + {u_2}^2 + {u_3}^2 ...
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381 views

Is there a time delay during tunnelling?

A particle hitting a square potential barrier can tunnel through it to get to the other side and carry on. Is there a time delay in this process?
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4answers
1k views

Decoherence and collapse

It is said that the decoherence does not solve the problem of measurement and/or the emergence of classicality, can somebody explain it with simple analogies or in a manner accessible to a ...
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3answers
1k views

Can we have discontinuous wavefunctions in the Infinite Square well?

The energy eigenstates of the infinite square well problem look like the Fourier basis of L2 on the interval of the well. So then we should be able to for example make square waves that are an ...
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165 views

knowledge of an internal observer

I would like to discuss the consequences of the concept of an internal observer in quantum theory. If we assume that we have a universe that evolves unitarily at a global scale and an observer is ...
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Nuclear/quantum physics simulation software

Is there any software which is able to simulate D-T interaction for example and get temperature-crosssection curve without referencing to any experimental data? Do we have quantum-level simulation ...
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Why water is not superfluid?

My question is in the title. I do not really understand why water is not a superfluid. Maybe I make a mistake but the fact that water is not suprfluid comes from the fact that the elementary ...
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349 views

How did QED diverge from quantum mechanics mathematically?

We have either Heisenberg or Schrodinger picture of quantum mechanics world. So, how did quantum electrodynamics come from mathematical formulations of quantum mechanics? Also, QED seems to have ...
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98 views

possible values of quantity in matrix mechanics

Suppose that there is a quantity described by the matrix as the following: $M = \begin{bmatrix} 3 & 0 & -i \\ 0 & 1 & 0 \\ i & 0 &3\end{bmatrix}$ How we determine possible ...
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235 views

Is Fractional quantum Hall effect proof that leptons are composite particles?

The fractional quantum Hall effect (FQHE) is a physical phenomenon in which the Hall conductance of 2D electrons shows precisely quantised plateaus at fractional values. Should this be considered ...
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Is Heisenberg's matrix mechanics or Schrödinger's wave mechanics more preferred?

Which quantum mechanics formulation is popular: Schrödinger's wave mechanics or Heisenberg's matrix mechanics? I find this extremely confusing: Some post-quantum mechanics textbooks seem to prefer ...
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Maxim Raykin's “solution to the measurement problem” using infinitely many derivatives

Recently I was made aware of the following arXiv preprint by Maxim Raykin: Analytical Quantum Dynamics in Infinite Phase Space. As far as I understand it, Raykin's idea is to reinterpret quantum ...
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443 views

When differential equation like Schrodinger is separable in some coordinate system?

When differential equation like Schrodinger is separable in some coordinate system? What needs to satisfy the potential ?
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Conservation Laws and Symmetries

Usually, in Quantum Mechanics, an observable is an operator on the space of the possible quantum states (labelled as $|\psi\rangle$). If this quantity is conserved, in the meaning that the associated ...
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654 views

Matrix mechanics for those with wave mechanics background

Just curious: Is there any book or resource that teaches matrix mechanics (quantum mechanics) only without wave mechanics stuff - meaning that the book assumes wave mechanics background.
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Connection between first and second quantization

This is my question: In a book on many body quantum theory I came across equality between antisymmetrized many-particle state vector which, as you know, includes sum over permutations of product ...
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305 views

Quantum $n$-body problem

Is the quantum $n$-body problem as difficult as the classical $n$-body problem? Or quantum mechanics allows to get a simpler exact solution? Suppose there are 3 particles with uniform potential ...
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1answer
543 views

Matrix element in quantum mechanics

This is about a matrix element of a second quantized operator. Consider the operator $$ U=\sum_{\alpha\beta}U_{\alpha\beta}c^{+}_{\alpha}c_{\beta} $$ Something strange emerges if we calculate again ...
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What is the mass of a wave?

The slide called "QUANTA" here says that "One Quantum has a definite mass" and the picture shows a wave. So, What is meant by the mass of a wave?
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Finding $\psi(x,t)$ for a free particle starting from a Gaussian wave profile $\psi(x)$

Consider a free-particle with a Gaussian wavefunction, $$\psi(x)~=~\left(\frac{a}{\pi}\right)^{1/4}e^{-\frac12a x^2},$$ find $\psi(x,t)$. The wavefunction is already normalized, so the next thing to ...
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About Born's rule

I wanted to gain a better understanding of the Born rule to make my class on quantum mechanic feel less ad hoc. To do so I attempted to show that the version (1) given in my book is equivalent to the ...
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796 views

Even and Odd States of a 1D finite potential well

Is it possible for a particle trapped in a 1D finite potential well to evolve from a even state to an odd state and vice-versa? Why?
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281 views

Spooky action appears to contradict Relativity of time order of multiple events

It is well known that in special relativity observers can disagree on the time ordering of two events. It is also well known that entangled particles exhibit so called spooky action at a distance. ...
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2answers
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How do I figure out the probability of finding a particle between two barriers?

Given a delta function $\alpha\delta(x+a)$ and an infinite energy potential barrier at $[0,\infty)$, calculate the scattered state, calculate the probability of reflection as a function of ...
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698 views

Find Trace of Dirac Matrix

The matrices present in the Dirac equation must have the following properties: $\{a^j,a^k\}_{ab} = 2\delta^{jk}\delta_{ab}$ $\{a^j,\beta\} = 0$ $(\beta^2)_{ab} = \delta_{ab}$ How can one show ...
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745 views

Topological Order and Entanglement

I have a question about entanglement in condensed matter physics. It seems that topological order origins from long range entanglement, but what is long range entanglement? It is the same as long ...
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2answers
456 views

What are the solution spaces of Nonlinear Schrödinger equations?

As we know, the solution space of Schrödinger equation is a Hilbert space, however, what about it of Nonlinear Schrödinger equations such as $$i\partial_t\psi=-{1\over ...
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1answer
905 views

Why doesn't the Klein-Gordon equation allow for conservation of probability?

I read somewhere that the Klein-Gordon equation doesn't allow for conservation of probability. Can someone prove this mathematically?
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Is the expectation value always an eigenvalue?

Must the expectation value of an observable always be equal to an eigenvalue of the corresponding operator? I already know that 0 is not an eigenvalue, but are there any other examples?
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104 views

Why can one equate the the zeroth order coefficient with the initial state in time-dependent perturbation theory in quantum mechanics?

Setup In the typical treatment of time-dependent perturbation theory in quantum mechanics, one arrives at the set of equations $$ i \dot{a}^{(r + 1)}_m(t) = \sum_n \langle m |H_1(t)|n \rangle e^{i ...
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2answers
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Conservation of Energy in a magnet

When a permanent magnet attracts some object, lets say a steel ball, energy is converted into for instance kinetic energy and heat when attraction happens, and they eventually collide. Does this imply ...
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1answer
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Applications of the particle in a box and the finite square well

What are some "real" world applications of the particle in a box (PIB) and the finite square well (FSW) which are discussed in an intro quantum mechanics class? For instance, I know that the PIB can ...
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1answer
11k views

How do you change Planck's law from frequency to wavelength? [duplicate]

I have to derive Wien's displacement law by using Planck's law. I've tried but I come to a unsolvable equation (well I can't solve it) anywhere I look online it comes to the same conclusion, you need ...
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1answer
218 views

What is changed when proton has finite radius?

How the field and interactions are changed when we assume that proton has finite radius in atom for example? What gives the finite size effect? Is it the higher moments of multipole expansion?
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913 views

What happens with photon when it is slowed down substantially?

In a dispersive media light's velocity can change substantially. Imagine we can slow it down to near 0 what the wave would look like? Frequency of light does not seem to change even at v=0 (at least ...
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How does QM allow imaging of individual electron orbitals?

Question: Why does the uncertainty principle allow probing of characteristics specific to the electron orbital distribution? If you measure an electron's position/momentum, then after you measure ...