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 ...

learn more… | top users | synonyms (3)

1
vote
2answers
94 views

Hydrogen atom: potential well and orbit radii

I happened to open up an old solid-state electronics book by Sah, and in it he says: "it is evident that the electron orbit radius is half the well radius at the energy level En" The orbit radius is ...
1
vote
1answer
51 views

What causes radioactivity? Is it a quantum mechanical effect?

I'm just curious what causes radioactivity. I've been told that in the case of alpha decay, since the nucleus is quantum mechanical, there is a probability that the configuration of protons and ...
2
votes
2answers
77 views

Aharonov-Bohm Effect electricity generation

This question is based on highly intuitive picture of the Aharonov-Bohm effect (perhaps a naive one). From what I have read, the current explanation of the AB effect is that although the electron ...
1
vote
3answers
50 views

Can stimulated emitted photons be absorbed?

Typically a stimulated photon will be one of a pair with its stimulating photon. If the leading photon is absorbed by a particle in the ground state, will it then be re-emited by the stimulated ...
0
votes
0answers
51 views

Philosophical thoughts on Reconciling Different Relativity and Quantum—Motivation behind String Theory [on hold]

I always like to reason through the motivation behind equations, and during this process I began thinking about Wigner's 'unreasonable effectiveness of mathematics', and whether it can sometimes lead ...
0
votes
1answer
29 views

Wave packets and amplitude

If a wave packet is given by: My question is basically how do we choose the write $A(k)$ to fit the particle we are looking at, or does it not matter (as my matter as my textbook seems to imply) ...
4
votes
2answers
154 views

Pauli's Exclusion Principle

Can someone tell me how Pauli's Exclusion Principle gives stability to matter? I know two electrons cannot occupy the same energy state so that is why we cannot squeeze bulk matter after a limit and ...
4
votes
1answer
264 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 ...
3
votes
3answers
634 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 ...
3
votes
1answer
59 views

Spin drift velocity?

I am currently reading this Phys Rev paper by H C Torrey. In this paper, he derives the Bloch equations with an additional diffusion term. He says that the current density is given by $$\mathbf ...
0
votes
0answers
28 views

Can observables with discrete and continous eigenvalues be commuting?

In Dirac's The Principles of Quantum Mechanics he often uses the notion of "a complete set of commuting observables". This means a set of observables $\{\xi_1, \xi_2, \ldots, \xi_v, \xi_{v+1}, \ldots, ...
1
vote
5answers
2k views

Reason for the Gaussian wave packet spreading

I have recently read how the Gaussian wave packet spreads while propagating. see: http://en.wikipedia.org/wiki/Wave_packet#Gaussian_wavepackets_in_quantum_mechanics Though I understand the ...
2
votes
2answers
415 views

an example of a quantum system for which wigner function transitions to negative values

I want to check my understanding of the Wigner transform and try to understand why and how exactly the probabilistic interpretation drops down as the function goes to zero and then to negative values ...
1
vote
2answers
144 views

Wigner characteristic function

I came across the "representation of a Gaussian state by its Wigner characteristic function". I don't know what Wigner characteristic function is and google results are not precise enough. Neither ...
0
votes
1answer
27 views

(Level: Undergrad) Continuity Conditions on the Wavefunction and Initial Values

I know that a physically meaningful $\Psi$ needs to be continuous. However, recently I came across a problem in which they were considering a wavefunction for the infinite square well potential and ...
0
votes
0answers
24 views

Mathematical derivation of interference pattern for electrons?

One of the most famous experiments in quantum mechanics in the context of wave-particle duality is certainly passing a beam of electrons through two slits, which results in an interference pattern ...
0
votes
2answers
27 views

If outside a cylindrical solenoid exist an electrical field what does that mean to the Aharonov-Bohm Effect?

To the question "What is the electric field outside a cylindrical solenoid when inside is turned on a magnetic field" the answer is that outside exists a electric field. Does that mean that the ...
0
votes
0answers
15 views

What is the most general definition of a bosonic Gaussian state?

I am reading this paper where the definition of the bosonic state is mentioned on page 2 here :- http://arxiv.org/pdf/0806.1625.pdf . From a general definition of any density operator in terms of ...
3
votes
5answers
197 views

About the definition of expectation value in quantum mechanics

In quantum mechanics, the expectation value of a observable $A$ is defined as $$\int\Psi^*\hat A\Psi$$ But in probability theory the expectation is a property of a random variable, with respect to a ...
0
votes
1answer
57 views

Showing Dirac equation's Lorentz invariance and use of unitary matrix $U$

Dirac equation is $i \hbar \gamma^\mu \partial_\mu \psi - m c \psi = 0 $ To show its Lorentz invariance, we convert spacetime into $x'$ and $t'$ from $x$ and $t$ and then $( iU^\dagger \gamma^\mu ...
0
votes
2answers
75 views

Why angular momentum about three independent axes?

The generic commutation relations for the angular momentum operator are $[J_x, J_y] = i \hbar J_z$, where the $J_i$, $i = x,y,z$ are the components of the angular momentum vector operator, $\mathbf ...
1
vote
1answer
65 views

How to compute observables from the boson field operator?

I think I understand that if given the two boson wavefunction of two different states \begin{align} \Psi(\boldsymbol{r}_1,\boldsymbol{r}_2) = \dfrac{ \psi_1(\boldsymbol{r}_1)\psi_2(\boldsymbol{r}_2) + ...
0
votes
1answer
83 views

Quantum states and state vectors

Does a state vector correspond to only one quantum states and the components in the state vector correspond to different states of this quantum state or is it that the components of the state vector ...
0
votes
2answers
60 views

What is the electric field outside a cylindrical solenoid?

What is the electric field outside a cylindrical solenoid when inside is turned on a magnetic field? The question is related to the question aharonov-bohm-effect-electricity-generation
-1
votes
0answers
16 views

why does muon hop rate in metals change with temperature like this

you can find this figure in this pdf we use μSR to study the superconductor properties,,but I don't quite understand the T^-9 slope, does muon trapped in an interstitial site and hop rate drop with ...
2
votes
1answer
160 views

number of gravitons launched by a proton

The wikipedia article http://en.wikipedia.org/wiki/Gauge_bosons describes how in QM exchanges of gauge bosons carry force, and describes how the graviton may also be a gauge boson. If the observable ...
0
votes
1answer
38 views

Connection to spin 1/2 electron system?

In another Physics stack exchange thread here, Spin matrix for various spacetime fields I obtained the generator of rotations of the SO(2) rotation group for an infinitesimal rotation of 2D vectors. ...
1
vote
0answers
27 views

How to derive equation for probability current density in relativistic quantum mechanics [on hold]

How does one derive equation for probability current density in relativistic quantum mechanics? I am asking for textbook-styled explicit derivation. No need for any other background knowledge.
0
votes
1answer
66 views

Are operators in quantum mechanics linear transformations?

Observables in quantum mechanics correspond to self-adjoint linear operators. If $\psi$ is an eigenvector of $\hat A$, then $\hat A\psi=\alpha\psi$ where $\alpha$ is the eigenvalue of $\psi$. ...
1
vote
2answers
57 views

Why diaphragm in diffraction experiment using electrons is quantum object?

In the book Quantum Mechanics - Volume 1 written by Albert Messiah, page no. 142-143, author says: ...But the diaphragm is a quantum object, just like the electron. Its momentum is not defined to ...
2
votes
2answers
77 views

Expanding a ket in the position basis?

My textbook says that to find the ket $|ψ\rangle$ in the same position basis as the ket $|ø\rangle$ we do the following: $$|ψ\rangle=\int dø|ø\rangle \langle ø|ψ\rangle$$ Firstly can $|ø\rangle$ be ...
3
votes
0answers
32 views

Spontaneous breaking of a discrete non-Abelian symmetry

Can someone give an example of an one dimensional local gapped quantum lattice model with a discrete non-Abelian global internal symmetry that is spontaneously broken in the ground state? In ...
0
votes
1answer
36 views

Fock matrix elements for RHF formalism

Here I refer to a particular book Molecular Quantum Mechanics by Peter W. Atkins and Ronald S. Friedman, but similar derivation could be found in many other texts. So, when obtaining the explicit ...
2
votes
2answers
170 views

Double-slit expirement fundamentals (half-silvered mirror version)

In the double-slit experiment variation in which 2 half-silvered mirrors and 2 mirrors are used to illustrate the interference of a stream of photons or single photons at a given time step, how is it ...
1
vote
2answers
117 views

What are correlated magnetic moments?

My book has the following sentence and I don't understand what correlation or lack of correlation means: At high temperature the magnetic moments of adjacent atoms are uncorrelated (to maximize ...
1
vote
1answer
69 views

The Eigenstate Existence Problem in Dirac's 'Principles of Quantum Mechanics'

In Chapter II of Dirac's Principles of Quantum Mechanics, Dirac explains that in general it is very difficult to know whether, for a given real linear operator, that any eigenvalues/eigenvectors exist ...
1
vote
0answers
47 views

Complete description of two electrons with spin

We have two electrons described by the wave function $\phi(\vec{x}_1,\vec{x}_2,s_1,s_2;t)$ where $\left| \phi(t)\right\rangle$ is the state vector and $(\vec{x}_1,\vec{x}_2,s_1,s_2)$ is the index of ...
3
votes
2answers
100 views

What is the analogy of $|x\rangle$ in quantum field theory?

Let me start from path integral formulation in quantum mechanics and quantum field theory. In QM, we have $$ U(x_b,x_a;T) = \langle x_b | U(T) |x_a \rangle= \int \mathcal{D}q e^{iS} \tag{1} $$ ...
0
votes
2answers
40 views

Do randomness and indeterminacy in Quantum Physics mean the same?

I have been trying to learn about the randomness in Quantum Physics. But of the many sources I referred to, some say about "Randomness in Quantum physics" and some others say about "Quantum ...
1
vote
4answers
134 views

If wavefunction is just a probability function, how does an electron interfere with itself

I have read lots of quantum mechanics books. The chapters that are talking about De Broglie, lots of them name the chapter as "Wave-particle duality" and says: "Electrons are both waves and ...
2
votes
1answer
48 views

What are the proper domains of the position and squared angular momentum operator?

I am looking at the position operator on a compact set $K \subset \mathbb{R}^n$ and the squared angular momentum operator (so essentially the Laplace-Beltrami operator where I just look at the angular ...
0
votes
1answer
48 views

How can we “know” that system interacted with another system or environment in quantum mechanics/decoherence?

I might be raising measurement problem in quantum physics in different words, but I will ask the question. Quantum decoherence has been proposed by proponents as a theory that eliminates all weird ...
0
votes
1answer
31 views

Solving particle on a ring problem using momentum eigenvalue equation instead of energy eigenvalue equation

I have read somewhere that for particle on a ring problem you don't have to solve eigenvalue equation $H\psi=E\psi$ you can instead solve eigenvalue equation $P\psi=p\psi$ where P is momentum ...
0
votes
2answers
61 views

Estimating the radius of the Hydrogen atom

I've seen people estimate the Bohr radius using the uncertainty principle by assuming that $$\Delta x \sim r$$ and $$\Delta p \sim p$$ then $$p \approx \frac{\hbar}{r}$$ Using this assumption will ...
1
vote
2answers
77 views

Given eigenvalues of $\vec l^2$ and $\vec s^2$, calculate the eigenvalue for $\vec j^2$

There was an exam question that read approximatly: Let $\vec j = \vec l + \vec s$. Given eigenvalues of $\vec l^2$ and $\vec s^2$, calculate the eigenvalue for $\vec j^2$. We came up with $$\vec ...
2
votes
2answers
112 views

A rigorous treatment of distributions in quantum mechanics

In many introductory courses to quantum mechanics, we see $\delta$-functions all over the place. For example when expressing an arbitrary wave function $\psi(x)$ in the basis of eigenfunctions of the ...
1
vote
0answers
64 views

How should a math undergrad student prepare himself to study GR and QM? [duplicate]

I'm quite sure that similar questions like this have been asked for more than thousands of times on here but since each person's background and interests are unique I believe questions like this ...
16
votes
2answers
530 views

Hilbert Space of (quantum) Gauge theory

Since quantum Gauge theory is a quantum mechanical theory, whether someone could explain how to construct and write down the Hilbert Space of quantum Gauge theory with spin-S. (Are there something ...
4
votes
1answer
147 views

Saturation of the Cauchy-Schwarz Inequality

Going to as little details as possible, here is a statement from Wald's text on QFT in curved spacetimes(I am not quoting the book) He considers two vector spaces ${\cal S}$ and ${\cal H}$. Note ...
4
votes
1answer
538 views

Two photons transition

if an atom in its ground state is coupled to an electromagnetic field it can absorb a photon if the EM field contains one with the right frequency. These transitions depends on $⟨f|H_i|i⟩$ (from ...