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

Inverse of Wave Reduction

Let's consider a system of three apparatuses. Sequentially these act as A device that measures momentum of an electron Parallel plates where electric field between them changes randomly. Same device ...
0
votes
0answers
8 views

Configuration Interaction for Hydrogen Molecule

Reading a book (do I need to cite?)on Quantum Chemistry, it introduces Configuration Interaction using excited slater-determinants in an Ansatz for a molecuar wave function. So the wave function will ...
0
votes
1answer
35 views

The Quantum Hall Effect

In the integral quantum Hall effect, one has that in regions where $_{Rxy}$ (the Hall resistance) is a constant, $R_{xx}$ surprisingly goes to zero. Why does that happen? Do impurities in the material ...
0
votes
1answer
59 views

Quantum mechanically, is superposition a sum or a product?

This question may sound like a no-brainer, but I'm getting confused after watching this lecture (cf. the slide at minute 5:07). The context is to motivate the quantization of a field which, for the ...
0
votes
1answer
54 views

Question about some symbols in quantum mechanics

I'm tring to understand some symbols in physics formula for example in Ehrenfest’s theorem $$\frac{\partial}{\partial t}\langle \hat Q \rangle = \left\langle \frac{\partial \hat Q}{\partial t} \right\...
0
votes
1answer
22 views

Does the minimum slit width change with different photon frequencies?

Send white light through a vertical polarizer and then through a second horizontal gap that is just wide enough to let all the light through. Now slowly close the second gap until it becomes a slit. ...
1
vote
1answer
23 views

Inversion symmetry on surface and spin

Let us assume you have a 3D bulk periodic crystal which has inversion symmetry e.g. $r\rightarrow -r$. Assume we are considering spinful operators with $S=1/2$. Now let us imagine cutting a surface ...
1
vote
1answer
35 views

Applying a rotation on an entangled state

I want to understand an experiment but I am struggling with the (basic) math/braket notation. In the experiment two ions are entangled and separated into two wells $A$ and $B$. The spin state of the ...
-2
votes
0answers
21 views

$\{|φ_i\rangle,|Χ_i\rangle\}$ is a basis set of Bi-orthogonal system. then please answer following

${|φ_i\rangle,|Χ_i\rangle}$ is Bi-orthogonal system, where $|φ_i\rangle,|Χ_i\rangle$ are from Hilbert space and Dual of Hilbert space respectively. My query is where do the $\langleφ_i |$ live?, ...
2
votes
1answer
34 views

What are the 'good' quantum numbers for the weak- and strong-field Zeeman effect?

I'm quite confused on the 'good' quantum numbers. I thought the good quantum numbers could be defined as the quantum numbers which corresponding operators commute with each other and the Hamiltonian. ...
2
votes
0answers
27 views

What happens to the electron when it is jumping between energy levels? [duplicate]

I intuitively thought that electron goes from one energy level to other just like we climb on stairs.. But I recently studied that electron do not exists between the jump.It vanishes at one energy ...
1
vote
1answer
44 views

Is Bohr's postulate really necessary from classical perspective?

Quoting the first sentence of the first postulate on wiki: The electron is able to revolve in certain stable orbits around the nucleus without radiating any energy, contrary to what classical ...
1
vote
0answers
38 views

Coherent state of “generalized” annihilation operator

We all know that the coherent state $|\alpha \rangle=\sum_n \, \frac{\alpha^n}{n!}\,(a^{\dagger})^n \, |0\rangle $ is an eigenstate of the annihilation operator: $a |\alpha\rangle = \alpha |\alpha \...
-1
votes
0answers
35 views

Find out the order of excited state of the electron in that state [closed]

The energy of an electron constrained to move in a one-dimensional box of length 0.4nm is 603.178eV. Find out the order of excited state of the electron in that state.
4
votes
3answers
976 views

Is Planck's Constant Really a Constant?

I am going through Groenewold's theorem and in his book: On The Principles of Elementary Quantum Mechanics, page 8, eq. 1.30: $$[\mathbf{p}, \mathbf{q}]=1\left(\text { i.e. } \mathbf{p q}-\mathbf{...
0
votes
0answers
52 views

A precise formula for the summation of an inner product

We have $2$ strings $|v\rangle$ and $\langle u|$, String $-1$ : $$|v\rangle=|e_{1}\rangle^{np}|e_{2}\rangle^{n(1-p)}$$ where : $e_{1}$ occurs $np$ times $e_{2}$ occurs $n(1-p)$ times ...
1
vote
3answers
45 views

If quantum Liouville's equation describes nonequilibrium evolution of the density matrix, why its derivation assumes time-independent probabilities?

For an ensemble characterized by the states $\{|n\rangle\}$ with probabilities $p_n$ at time $t$, the density operator is defined as $$\rho\equiv \sum\limits_n p_n|n\rangle\langle n|.$$ Assuming that ...
0
votes
2answers
51 views

Deriving the quantum Hamiltonian from the expression of classical energy

I am currently learning about the Dirac formalism in quantum mechanics, but don't quite understand how we derive the expression of the quantum Hamiltonian, given the value of energy in classical ...
1
vote
0answers
48 views

Are there any textbooks with very thoughtful quantum mechanics problems? [closed]

David Morin's book on classical mechanics is one of my favourite textbooks because of the amount of care that went into constructing the amazing end-of-chapter problems. I haven't found anything ...
1
vote
1answer
52 views

What is Quantum Cosmology

I understand that quantum behavior is only apparent on the microscopic level, what then is the subject of Quantum Cosmology?
1
vote
2answers
78 views

Minimal coupling in Dirac equation

In the framework of relativistic quantum mechanics (not QFT) the Dirac equation in presence of external electromagnetic field is obtained by means of the minimal coupling, i.e. the substitution: $$p_{...
6
votes
1answer
58 views

Which is the state of the art of relativistic many-body QFT?

We have a class of relativistic quantum field theories, typically used to calculate particle interactions (scattering) or to extend the Standard Model. Typically one start with a "free" theory, then ...
0
votes
0answers
21 views

What is the actual uncertainty principle formula? [duplicate]

I found two different versions of the uncertainty principle in different books. In some it is written as $\Delta x\Delta p\ge\hbar$, while some others use $\Delta x\Delta p\ge\frac{\hbar}{2}$. I'd ...
1
vote
0answers
34 views

Expression for sum over paths

In an introductory lecture on the path integral formalism, I came across the following. Suppose that $\gamma$'s are paths such that a particle travelling along any of them reaches the position co-...
1
vote
2answers
77 views

What happens to the uncertainty principle if

I just read the Feynman Lectures about the electron gun experiment with two holes in the middle wall. It demonstrates that if we don't look at the electrons while they travel toward the detector ...
2
votes
1answer
25 views

Will entropy continue to increase in an accelerating-expanding universe?

Before/at/during the Big Bang, quantum fluctuations progressed until there was a constant energy density somewhere which caused inflation. The slight variations in energy due to those quantum ...
0
votes
1answer
34 views

Measuring a state in a basis other than eigenbasis

Suppose I have a state expressed in its eigenbasis as follows. $\rho = \sum_i\lambda_i\vert i\rangle\langle i\vert$. It is now measured in some other basis $\{\vert x\rangle\}$ that is distinct from ...
0
votes
0answers
12 views

Application of geometric phase in physics [closed]

Well, I have just studied geometric phase in quantum mechanics. Can anyone provide any applications of it? I read Wikipedia, and it says "The geometric phase provide a unified theory to many aspects ...
0
votes
0answers
19 views

Number of bosons and fermions in the fundamental irreducible massive multiplet

The fundamental irreducible massive multiplet is given by $$\Omega^{(n)\alpha_1\cdots \alpha_n}_{\;\;\; A_1 \cdots A_n}=\frac{1}{\sqrt{n!}}\left(a^{A_1}_{\alpha_1}\right)^\dagger \cdots \left(a^{A_n}_{...
1
vote
0answers
16 views

Measurement of observables of a gas in a weakly interacting room

Suppose I have a gas at equilibrium in a box weakly interacting with the room (weak exchange of energy but absolutely no exchange of particles, so that we are in a canonical ensamble). The gas ...
2
votes
1answer
36 views

Does the spatial part of the wavefunction need to be antisymmetric in the singlet and symmetric in the triplet?

Two spin-1/2 particles either are part of a spin-1 triplet or a spin-0 singlet. The singlet is antisymmetric but bosons need to be symmetric wave functions. So does the spatial part of the wave ...
0
votes
0answers
44 views

Evaluating expectation value in second quantization using Wick's theorem

I am working in the context of quantum chemistry. Given this expectation value in second quantization $$ \langle 0 \vert [p^\dagger q, \kappa] \vert 0 \rangle $$ with $$ \kappa = \sum_{ai} k_{ai}(a^...
1
vote
1answer
38 views

Self-adjoint operators on $\mathbb{C}^2$

I want to show that self-adjoint operators in a complex space of dimensions 2 does form a real vector space. It seems a very simple questions, but then I realize that I am not sure of how to represent ...
0
votes
1answer
83 views

What exactly is meant by a “time-reversed Hamiltonian”

For context, I am reading this paper. Basically, the paper makes reference to "evolving with respect to the time-reversed Hamiltonian". I'm slightly unclear as to what this actually means. Here is my ...
0
votes
2answers
75 views

What is the probability of finding a specific value of energy? [closed]

knowing that energy is given by $E_{n}=\frac{n^{2}\pi^{2}\hbar^{2}}{2ma^{2}}$ and that $$|\psi(t=0)\rangle=\frac{1}{\sqrt{6}}|\phi_{1}\rangle+\frac{1+i}{\sqrt{12}}|\phi_{2}\rangle+\frac{1-i}{\sqrt{4}}...
1
vote
0answers
20 views

Information loss problem if almost perfect black body

Assume a almost perfect black body at temperature zero and consider pointing a signal, let's say a laser beam (pure state), on this body. What happens with the information of the beam? My thoughts go ...
0
votes
0answers
71 views

How to express a rank-2 tensor as a spherical tensor?

A common example how to write a rank-2 tensor in the spherical basis is an outer product of two vectors, $$ T_{ij} = a_i b_j $$ such that $$ T_{ij} = \frac{\textbf{a}\cdot\textbf{b}}{3}\delta_{ij} + ...
1
vote
0answers
55 views

How many measurements does it take to determine a quantum state?

Suppose I have a wave-function over a Hilbert-space of (complex) dimension $N$. It has $2 N-2$ real degrees of freedom, after normalization and removing the phase. It seems to me that I can measure ...
0
votes
1answer
43 views

Second quantization: periodicity of annihilation and creation operators in momentum space, originally on a lattice

I have a Hamiltonian $H$ on a periodic lattice, which is expressed as, say: $$H = \sum_{n} (A_n a^\dagger_n a_n + B_n a^\dagger_{n+1} a_n + h.c.)$$ where $A_n$ and $B_n$ are periodic in space (over ...
0
votes
1answer
145 views

What is more fundamental: Fock space or Hilbert space? And why?

Consider the following state for some bosons represented in Fock space: $$|2\rangle_{k_1}|1\rangle_{k_2}$$ where $k_i$ is some distinguishing index. You may think of these as the two different ...
-1
votes
0answers
12 views

Finding the potential energy surface for a given configuration of atoms reference? [closed]

Just curious if somebody is aware of a good reference that shows the construction of a potential energy surface for any set of atoms, because I was interested in the idea of how such a function is ...
0
votes
1answer
53 views

Question regarding Wightman's “transformation law” axiom for QFT

On the Wightman axioms Wikipedia page, the W2 axiom describes the effect of Poincare transformations on the quantum field. It states: $$U(a,L)^\dagger A(x) U(a,L)=S(L)A(L^{-1}(x-a))$$ where A is the ...
1
vote
0answers
40 views

Density of States (DOS) to energy graph

I am trying to find the amount of electrons in a conduction band in Si (Silicon), all I've got is a graph similar to this one: I've tried to integrate like this: $$ N = \int_{1}^{\infty} \frac{1}{1+\...
1
vote
2answers
71 views

Is symmetrization $xp-px$ required for commutation $[H,x]=0$?

Given a Quantum Hamiltonian: $$\hat{H}=ax^2+bp^2$$ It does not commute with either $x$ or $p$. Suppose we have a Hamiltonian :$$H = k \hat{p}\hat{x}$$ why do we need it to be: $$H = k (\hat{p}\hat{x} -...
0
votes
0answers
31 views

Discrepancy in Legendre function for angular momentum [closed]

On wikipedia: https://en.wikipedia.org/wiki/Associated_Legendre_polynomials It is clear that the formula to solve for the eigenfunctions of $\hat{L}^2$ are the spherical harmonics where: $$ Y_{l, m} ...
1
vote
1answer
55 views

What is the anti-normally-ordered representation $\hat \rho_A$ of a state $\hat\rho$?

While reading the Wikipedia page on the P function, I came across the following consideration (paraphrasing from there): Given a state $\rho$, if we write it in anti-normal order as $\rho_A=\sum_{...
3
votes
1answer
83 views

How Translation Operator is defined?

Here, In Shankar's (2nd edition, p-283) QM book, The translation operator is given by $$T(\epsilon) = I - \frac{i\epsilon}{\hbar}G \tag{11.2.13}$$ Similar In Sakurai (Revised edition 1994 p-45), he ...
-1
votes
0answers
35 views

What is $[\hat{x},\hat{p}^2]$? [closed]

The way I calculated it was as follows: $$[\hat{x},\hat{p}^2] = [\hat{x},\hat{p}]\hat{p} + \hat{p}[\hat{x},\hat{p}] = i\hbar \frac{\hbar}{i} \frac{d}{dx} + \frac{\hbar}{i} \frac{d}{dx} i\hbar = i\...
1
vote
1answer
25 views

Double slit experiment with different paths - How to make such an experiment?

In the double-slit experiment, if we could make the electron traveling through slit $A$ to travel longer distances then the electron traveling through slit $B$, what would be the result? I was trying ...
0
votes
1answer
26 views

The Aharonov-Bohm effect for arbitrary $B$-field

The Aharonov-Bohm effect is discussed for the case of particles moving along a closed loop through a region with zero magnetic field, however I was wondering whether it still holds for arbitrary ...

1
2 3 4 5
405