Questions tagged [quantum-mechanics]

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-theory tag for the theory of many-body quantum-mechanical systems.

Filter by
Sorted by
Tagged with
0
votes
0answers
8 views

How can i obtain the the correction to the eigenvalues as a result of adding the gravitational potential to the hydrogenlike atom?

In treating the hydrogen-like atoms, we normally neglect the gravitational potential for the system. I am able to justify the above statement by comparing the gravitational potential to the ...
0
votes
0answers
15 views

Confusion regarding the bound state of a Delta-function potential and Tunneling

I was reading (Griffith's QM book) about the Bound states for delta-function potential of the form $-\alpha \, \delta(x)$ where $\alpha > 0$. I feel a bit conceptually unclear. Few doubts I have ...
0
votes
0answers
11 views

Double Slit Eraser - does the wave function collapse and restore or never collapse

This video shows a rudimentary double slit eraser experiment. He sends photons through a double slit with a polarization film before the double slits (with a 90 degree difference) to obtain "which-way"...
1
vote
1answer
22 views

Derivation using reduced mass for electron orbitals in the Bohr model [duplicate]

Recently in my class, we used the Bohr model to consider the motion of the nucleus about the center of mass of the electron-nucleus system. I understand that this also happens in the Earth-moon system,...
0
votes
1answer
26 views

Interaction picture Sakurai

I’m going through Sakurai and got stuck with the following in the interaction picture subsection $$i \hbar \frac{\partial}{\partial t}\left|\alpha, t_{0} ; t\right\rangle_{I}=i \hbar \frac{\partial}{\...
5
votes
3answers
272 views

Which basis does the wavefunction collapse to?

When we measure position for example, how does the system "know" that we're measuring position in order to collapse to a position eigenvector? Does the wave function always evolve from the state that ...
0
votes
0answers
25 views

Scully’s DCQE paper 1999 - reasons for phase shift

http://Arxiv.org/abs/1103.0117 Or better Google the paper using string: arxiv:quant-ph/9903047v1 In order to “see” (detect) the interference pattern we have to take care about the shift of Lambda ...
0
votes
1answer
33 views

Dispersion under Classical and Quantum regimes

If I understand correctly the literature on dispersion, the atom is modeled as an electron bound to an atom by a spring with the electron behaving as a driven, damped oscillator. The electron ...
1
vote
1answer
34 views

Definition of electron density in DFT

I read that the electron density used for density functional theory in a system of $N$ electrons with wavefunction $\psi$ is defined as $$\rho(r)=N\int d^3r_2\dots d^3r_N \psi^*(r,r_2,\dots r_N)\psi(...
0
votes
1answer
89 views

Which wave function should I adopt?

Suppose I have Hamiltonian $H_0(\hat{p},\hat{r})$, it satisfies $H_0\psi(p,r)=E(p)\psi(p,r)$. If I make a change from $\hat{p}\to\hat{p}+p_0$, what is the form of the wave function of the Hamiltonian $...
0
votes
0answers
31 views

Infinitesimal Perturbation in a potential well

If I calculate $<\psi^0|\epsilon|\psi^0>$ and $<\psi^0|-\epsilon|\psi^0>$ separately fro two different intervals, viz. 0 to $\Delta$ and from $a-\Delta$ to $a$ and then add, the ...
-1
votes
0answers
23 views

What constitutes a quantum mechanical state? [duplicate]

In quantum mechanics, what exactly is the "state" of a quantum system and what constitutes the "state" of a quantum system? i will appreciate an intuitive and as well a mathematical answer.
-1
votes
0answers
37 views

Energy Eigenvalues from a given Hamiltonian [on hold]

Consider the Hamiltonian, H=σX Where σ=(σx, σy, σz) is the Pauli Vector with the respective Pauli Matrices and X=(x,y,z) is the position vector. What will be the Energy Eigenvalues for the given ...
0
votes
1answer
47 views
1
vote
0answers
38 views

Bell's theorem dichotomy

I've read a few texts about Bell's theorem where the following is claimed: Modern formulations of quantum mechanics must incorporate Bell’s result at their core: either they refuse the idea that ...
-1
votes
0answers
50 views

Inside the singuarity

This thread may be off-stream physics but it is related to a very interesting subject . What happens to the centre of a black hole ? Do quantum effects become dominant or is GR totally correct? ...
0
votes
0answers
27 views

New locution regarding perturbation theory

I am trying to make a sentence more approachable to a general audience by not using technical language. I fear I'm however losing precision in this new language. Original sentence: The use of ...
1
vote
0answers
26 views

Incompatible equations of motion in non-Hermitian (PT-symmetric) model

There is an interesting paper on Goldstone theorem of non-Hermitian QFT. arXiv:1808.00437. On page page 8-9 equation (36)-(38), author says that having equations of motion that are NOT complex ...
0
votes
1answer
98 views

A Schrödinger Love Poem? [on hold]

This question is for those who can see the romantic side of the Schrödinger equations... My GF is studying quantum mechanics, and I was thinking to write it as an expression of a two-particle ...
-1
votes
0answers
34 views

How does angular momentum get quantized? [duplicate]

We know that the magnitude and direction of angular momentum is quantized in quantum mechanics. We can explain the quantization with the help of quantum numbers. But actually who is responsible for ...
1
vote
1answer
34 views

Why do we see particles in the many-worlds interpretation?

I am starting to feel like I have a decent grasp on the MWI, but a piece of it keeps bugging me. My understanding is that quantum objects are kind of spread out and wavy until something comes along ...
0
votes
0answers
32 views

Interaction between electrons obeying Pauli's exclusion principle

For fermions having half spin, obeying Pauli's exclusion principle, we know that for states with different spin states, the particles (say electrons) are distributed in such a way that if the first ...
0
votes
2answers
49 views

Solution of Time-dependent Schrodinger Equation for Unitary Operator

While reading Quantum Mechanics Book by Sakurai, I found the time-dependent Schrodinger equation for Unitary Operator. $$i\hbar \frac{\partial}{\partial t}\mathcal{U}(t,t_0)=H\mathcal{U}(t,t_0).$$ ...
1
vote
0answers
40 views

Wavefunction of particle in power law potential of type $x^a$?

How could we calculate the wave function of a particle under a potential of form $V(x)=x^a$? Is there any analytical solution or any general feature of such solution (like its an exponential ...
0
votes
0answers
24 views

Interaction Hamiltonian in two electron system

Let's assume we have two electrons which are in three single particle state. I can write the total radial wave function for the spin state. Since interchanging particle in two particle fermionic ...
0
votes
1answer
31 views

Symmetry in the spin orbital coupling Hamiltonian

The spin orbit coupling and the extra perturbation in the Hamiltonian: $$H^\prime = a \ L \cdot S + b \ \ p\cdot r $$ a and b are constants. My plan is to check the continuous symmetry on the ...
2
votes
3answers
49 views

Does spin add energy to a quantum mechanical system?

If a particle (let's say an electron, a 1/2 spin particle) has spin component $S_z=\hbar/2$. Does the spin contribute to the total energy of the electron? For example, without considering the spin, ...
1
vote
1answer
27 views

Is every density moment of a quantum harmonic oscillator a classical harmonic oscillator?

Suppose we have the usual harmonic oscillator: $$ \hat{H}=\frac{\hat{p}^2}{2m}+\frac{1}{2}m\omega^2\hat{x}^2 $$ with an arbitrary initial state. It is well known that the first density moment $\langle\...
2
votes
2answers
75 views

Confusion about Stern-Gerlach experiment

Why does the particle always have the same spin magnitude $\pm \frac{1}{2}\hbar$? In classical mechanics we can split a vector into components but in quantum mechanics due to uncertainty principle ...
-1
votes
0answers
45 views

Can we say that most of Quantum mechanical interpretations are different only in placement of the Heisenberg cut? [on hold]

For instance, de Broglie-Bohm put the Heisenberg cut at the infinite past (or the initial conditions of the universe), Copenhagen at finite past, von Neumann at present, Relative QM at the finite ...
-1
votes
2answers
58 views

When does quantum entanglement cease?

On Wikipedia on Quantum entanglement: “However, this behavior gives rise to seemingly paradoxical effects: any measurement of a property of a particle performs an irreversible collapse on that ...
2
votes
0answers
58 views

Is every operator a power series of creation and annihilation operators (in a rigorous mathematical sense)?

Let $\mathscr{H}$ be a Hilbert space denoting the single-particle states and $c_k^*,c_k$ denote creation and annihilation operators of orthonormal basis $\phi_k\in \mathscr{H}$. Let $\mathscr{F}$ ...
0
votes
1answer
54 views

${}$ Dirac delta potential

We know that the number of bound states for an attractive delta potential is one. If so what will the number of bound states for a particle in a repulsive delta potential? If $V(x)= +a \cdot \delta(x)$...
2
votes
0answers
17 views

What is the difference between quantum sensing and quantum metrology?

The title is mostly self-explanatory. Both terms get thrown around a lot. I used to think quantum sensing uses harmonic oscillators / bosons and quantum metrology spins, but this doesn't seem to ...
1
vote
2answers
44 views

Confused regarding the special case “Wide deep well” of the Finite Square Well Potential in Griffiths book

I am assuming that some of the equations I write are known to you people as they are all from Griffiths. Let me know if something seems vague. So after solving the time-independent Schrödinger for ...
-4
votes
0answers
69 views

Quantum mechanics doesn't imply free will [on hold]

There is a belief that free will, the ability to choose between different possible courses of action unimpeded, is an effect of QM. But I think I found a counterproof: Quantum superpositions decay at ...
0
votes
1answer
58 views

Selection rules on quadratic terms

Let's assume I have to find expectation value of $z^2$ in the $|l_im_i\rangle$ state. Can I use the selection rules in this way? $$\langle 10|z^2|10\rangle$$ $$=\langle 10|z \color{red}{|10\...
0
votes
0answers
21 views

Numerical simulations of Landau-Zener transition

I tried to use a midpoint method and numerically solve the Schrödinger equation for the original Landau-Zener (LZ) problem: a 2X2 Hamiltonian $\begin{pmatrix}\alpha t&\delta \\ \delta &-\alpha ...
0
votes
0answers
37 views

Non-normalised Bargmann Coherent States

Currently, I am reading a paper which involves non-normalised Bargmann coherent states as my basis. I am interested in knowing how the creation and annihilation operator acts on these coherent states. ...
1
vote
1answer
69 views

What is $\frac{d}{d\psi}\langle\psi| \hat{O} | \psi\rangle$?

I would like to know what is the derivative of an expectation value with respect to the molecular state $$\frac{d}{d\psi}\langle\psi| \hat{\mathbf{O}} | \psi\rangle$$ Note that here $|\psi\rangle$ ...
-1
votes
2answers
55 views

What is the (triplet) eigenstate for two electrons? [duplicate]

Let's assume I have a harmonic oscillator which is one dimensional. What is my plan is to work the the two electron's spin states and my requirement is that they have to be in the triplet sates. Lets ...
0
votes
0answers
22 views

Wavefunction and associated energies of particle in uniform magnetic field [on hold]

I'm trying to find the wavefunction and associated energies of a charged particle in a uniform magnetic field . We have the following hamiltonian: $$ H = \frac{(-i\hbar\nabla -q\vec{A})^2}{2m} $$ ...
-4
votes
0answers
53 views

What are three predictions of quantum mechanics? [on hold]

Specifically discussing the phenomenon of photons traveling through polarizers, what predictions are made by quantum mechanics?Bell’s theorem says “No physical theory of local Hidden Variables can ...
1
vote
1answer
30 views

Can one have $\mathcal{PT}$-symmetry in a QFT theory proportional to an imaginary field?

There is a lot of fuss nowadays around $\mathcal{PT}$-symmetry in non-relativistic quantum mechanics. Recently I came across this paper where the authors generalize the non-relativictic Hamiltonian $$...
0
votes
1answer
66 views

Is There Already Evidence Supporting Stapp's Theory of the Causally Efficacious Human Will? [on hold]

Physicists J. Acacio de Barros and Gary Oas wrote a paper titled “Can we Falsify the Consciousness-Causes-Collapse Hypothesis in Quantum Mechanics?” published in the Foundations of Physics, 47(10):...
0
votes
0answers
18 views

Can we study the effects of Quantum reflection on heavy atoms?

From what I've looked at, it feels like QR has only been studied on light atoms like He, Ne, Na, H, etc. But can we study this effect on heavy atoms like Rb-87. If not, is it because of the ...
0
votes
2answers
82 views

Why does the lowering operator applied to lowest state have to be 0?

When solving a problem in QM with raising and lowering operators ($\hat{a},\hat{a}^\dagger,L_{\pm},..$) it is often assumed that: $$ L_-|\Omega>=0 $$ Why is this assumed? Couldn't the result ...
0
votes
1answer
42 views

Angular momentum operator transformation under rotation

The generators of rotations $J_i$ under rotation transform as $$J_i'=R_{ij}J_j\,.$$ Now $J^2=J_1J_1+J_2J_2+J_3J_3$ trasform as $$ \begin{aligned} J'^2&=RJ^2R^{-1}=RJ_1R^{-1}RJ_1R^{-1}+RJ_2R^{-1}...
-1
votes
1answer
101 views

Doubt in quantum mechanics

My lecturer said that when a oscillating body loses energy in the form of radiation the natural frequency of oscillation is equal to the frequency of the emitted radiation. Can someone explain why?
0
votes
0answers
23 views

Hamiltonian for a mode-shift operator

I have a discrete multi-level degree of freedom in my quantum system (for photons, for example this), which I write as $|l\rangle$. The degree of freedom is unbounded, i.e. $l$ can take ever positive ...