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 quantum-field-...

learn more… | top users | synonyms (4)

0
votes
2answers
75 views

The counter-intuitive time scales in atomic physics and nuclear physics

Compare atomic physics and nuclear physics. The interaction in the latter is much stronger than that in the former. However, the typical spontaneous emission time scale in atomic physics is on the ...
0
votes
1answer
55 views

Reduced Density operator in matrix form

I already read book of Quantum Computation and Quantum Information by Nielsen and Chuang according to reduced density operator and I already understand how to do the reduced density using Dirac ...
0
votes
1answer
33 views

How does a hydrogen ion gas cool?

Ok I understand that a hydrogen gas of non-ions at a temperature higher than its surroundings exists with many excited electrons. These electrons, either spontaneously or due to collisions, will ...
1
vote
2answers
88 views

How to form the matrix representation of $|O|^3$

I'm interested in getting the matrix representation of the absolute value of an operator. I know the matrix representation of the operator $O$. Now how do I take its absolute value?
1
vote
0answers
228 views

Intuition behind transforming a Hamiltonian expressed in momentum representation in eigenbasis [closed]

This question is a supplement to a previous question on the same paper. In the section 4.1 of Quantum Computation by Adiabatic Evolution, Farhi et al proposes a quantum adiabatic algorithm to solve ...
4
votes
2answers
200 views

why does the frequency of a wave remain constant?

They say the frequency of a wave is its fundamental character, thus remain constant throughout its propagation regardless the medium through which it travels. Could anyone explain why frequency of ...
3
votes
1answer
37 views

Reflection and refraction of single photon incident on a glass slab

If a single photon strikes a glass slab of certain thickness, can we make prediction whether it would reflect or refract? On which factor the reflection or refraction of single photon through such a ...
4
votes
2answers
77 views

Is there a relation between spin and the spin group?

In Quantum Mechanics spin appears as one type of angular momentum. Indeed, in Quantum Mechanics one angular momentum on the state space $\mathcal{E}$ is a triplet of observables $\mathbf{J}=(J_1,J_2,...
3
votes
1answer
60 views

What does partial (non-maximum) quantum entanglement mean?

When quantum systems are entangled, they have a "grade of entanglement" which can be quantified e.g. as the entropy of entanglement. There also are states of "maximum entanglement", e.g. the Bell ...
0
votes
1answer
42 views

Expectation energy for a quantum harmonic oscillator

At 59:14 in this video, the expectation value of the energy of a harmonic oscillator is $$ \langle E \rangle = \int ||\tilde{\Psi}(p)||^2 \frac{p^2}{2m}\ \mathrm dp + \int ||\Psi(x)||^2\frac{m\omega^2}...
2
votes
2answers
159 views

Quantum Operators: An Identity

I came across the following neat property: For an operator $\hat{A}$ which is a linear combination of creation and annihilation operators, we have: $$ \langle e^{\hat{A}} \rangle = e^{\langle \...
0
votes
1answer
41 views

Why does Carbon-12 have zero nuclear spin?

While studying NMR theory, my textbook explained that only nuclei with odd mass numbers are NMR active because they have non-integer spin quantum numbers and nuclei with an even mass number and atomic ...
3
votes
1answer
38 views

Protocol for solving time independent Schrodinger equation

Just a short question about the protocol for solving the time-independent Schrodinger equation for different potentials and the reasons for accepting and rejecting solutions. Take for example the ...
1
vote
0answers
45 views

How does the filling of the 2p orbitals occur?

When electrons enter the 2p orbitals, electrons of the same spin occupy the 2p orbitals first and then electrons of the opposite spin fill up the orbitals. Why is that? My professor told me that there ...
3
votes
2answers
165 views

Gauge transformation of vector potential multiplies wavefunction by phase

Consider an electron in an electromagnetic field with scalar and vector potentials $\phi, \mathbf{A}$. Suppose for simplicity that $\mathbf{A}$ is time independent. Suppose also that we know the ...
0
votes
0answers
23 views

WKB approximation to find energy levels of a step potential

Suppose the following potential: $$ V(x) = \begin{cases}V_0 & 0<x<\frac{a}{2} \\ 0 & \frac{a}{2}<x<a \\ \infty & \text{otherwise} \end{cases} $$ Also, assume that for every ...
2
votes
1answer
101 views

Can a particle pass through a point where wave function is zero?

Let's consider an infinite square well. In the first exited state there is a node at the middle of the well (i.e. wave function and thus probability of finding the particle is zero there). If I ...
0
votes
1answer
50 views

Can a quantum mechanical system have more than one wave-function?

I was told that a quantum mechanical system is completely determined by its wave function. But superposition principle says that given two wave functions of some system, a linear combination of them ...
2
votes
2answers
96 views

Why does a electric Potential have to be real, but not a Potential in quantum mechanics?

So I had this Problem when I had to learn about classical electromagnetism: Why is it, that we use complex numbers when calculating stuff, but in the end only the real part is important (for example ...
0
votes
0answers
36 views

“Instantaneous” time stepping with time dependent Hamiltonian Schrodinger equation

The Schrodinger equation for time-dependent Hamiltonian is $$i\hbar\frac{d}{dt}\psi(t) = H(t)\psi(t) \, .$$ I know that the "instantaneous" solution of this equation is $$\psi(t+dt) = e^{-\frac{i}{...
0
votes
1answer
45 views

Why Does there Have to be Linearity in Ket and Skew Symmetry?

I'm reading Shankar's "Principles of Quantum Mechanics," and on page 8 he states that one axiom in Dirac notation is linearity in ket, and because they are also skew symmetric there is anti-linearity ...
0
votes
2answers
29 views

Book Recommendation: Quantum optics

Could you suggest me a list of books for understanding Quantum Optics for students who have studied Introductory Q.M.(such as Griffiths). It would be grateful if you distinguish between readable one(...
0
votes
3answers
112 views

What is the cause of quantum entanglement? [duplicate]

I understand the idea of quantum entanglement - where what happens to one particle in one location instantly effects another particle in another location, even if separated by millions of miles. But ...
0
votes
0answers
28 views

Planck's temperature - why is there a maximum? [duplicate]

Why do the laws of physics break after Planck's temperature?
2
votes
1answer
36 views

Relationship Between Magnetic Dipole Moment and Spin Angular Momentum

I am reading Introduction to Quantum Mechanics 1st edition by David J. Griffiths and I have a couple questions about this section on page 160. A spinning charged particle constitutes a magnetic ...
0
votes
0answers
32 views

Identical bosons with spin interactions eigenstates

Suppose that we have two particles where each of them has s=1 and it is in a harmonic oscillator potential and there is also a spin interaction. The hamiltonian of the system is :$$H=\frac{p_1^2}{2m}+\...
2
votes
0answers
30 views

Distribution of quantum beating among spectral frequencies

Let's imagine that we have 3-level system: ground state $\vert 0 \rangle$ and two excited states $\vert 1 \rangle$, $\vert 2 \rangle$ with similar energies $\hbar \omega _1$ and $\hbar \omega _2$ ...
11
votes
1answer
234 views

Significance of the exception to Gleason's Theorem when n = 2

Gleason's Theorem famously asserts that (appropriately defined) measures on the lattice of a complex Hilbert space can be implemented by density operators via the trace operation, except in the case ...
2
votes
0answers
58 views

Rigorous way of box normalisation

This is follow up from an answer to my previous question about unitarity in rigged Hilbert space. As it turns out, that there is no idea of unitarity in rigged Hilbert space (hence no meaningful QM ...
3
votes
2answers
91 views

How to visualize an electron existing in two different places at the same time?

Let's consider a hypothetical situation where there are two electrons. The first electron is in superposition, simultaneously existing in two different locations. Let the locations be ...
5
votes
3answers
135 views

Can a physical wavefunction be non-smooth (its first derivative is discontinuous)?

Here's an argument that might support the statement that such a non-smooth wavefunction is not physical: You cannot add a finite number of smooth functions to get a non-smooth function. By fourier ...
1
vote
1answer
35 views

What is the angular velocity of the electron?

An electron has angular momentum. Shouldn't it also have angular velocity? Ignoring the g-factor (just for the order of magnitude approximation) and the fact that an electron is not a sphere the ...
2
votes
1answer
59 views

Norm preserving Unitary operators in Rigged Hilbert space

If we take the free particle Hamiltonian, the eigenvectors (or eigenfunctions), say in position representation, are like $e^{ikx}$. Now these eigenfunctions are non-normalisable,so they don't belong ...
2
votes
1answer
146 views

Strange implication of the relativistic invariance of the Dirac equation

At least as normally formulated, the law of transformation of a wave function solution of the Dirac equation to another inertial frame seems to indicate that if observer 1 is certain the particle is ...
0
votes
1answer
67 views

Understanding Quantum Harmonic Oscillator derivation

I'm using this pdf as a reference. Basically, I want to solve equation 0.3, which can be simplified to equation 0.5. The solution is in the form $$ \Psi(u)=h(u)e^{\frac{-u^2}{2}}$$ where $h(u)$ can ...
1
vote
0answers
41 views

Density of States for a separable hamiltonian

There are $N$ non interacting electrons in a potential well: \begin{align} H&= -{1 \over 2 } \nabla^2 + U(x,y,z) \\ U(x,y,z)&={1\over2}\omega^2z^2 \; \mbox{for} \; (x,y) \in [0,L]\times [0,L]; ...
2
votes
0answers
69 views

Free Particle: Time dependence of expectation value of position Paradox

It would be really appreciated if somebody could clarify something for me: I know that stationary states are states of definite energy. But are all states of definite energy also stationary state? ...
0
votes
1answer
72 views

An example of a nonlinear but deterministic physical transformation in Hilbert space

Supposedly all physically realisable transformations are either linear or non-deterministic (measurements are not linear transformations, but they are non-deterministic, from the perspective of the ...
1
vote
0answers
27 views

Normalize plane wave on an infinite domain.

I need to make an exercise related to quantum mechanics. (Specifically I need to apply Fermi's golden rule where the initial and final states are both plane waves). The system is 1 dimensional, ...
0
votes
0answers
42 views

At most $N$ gapless charge/spin modes in a system of $N$ coupled 1D chains?

Leon Balents and Matthew P. A. Fisher claimed the following without any further explanation ($N$ is the number of chains) For a system of $N$ coupled 1D chains, the number of gapless charge modes ...
0
votes
0answers
37 views

Current Conservation [on hold]

Why is current conservation important? Specifically, in QFT and String Theory lecture notes and textbooks it's always stated that current conservation is important because it helps maintain quantum ...