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 (4)

1
vote
0answers
13 views

Deriving effective model without integrating out degrees of freedom in path integral formalism?

In path integral formalism of quantum field theory (particle physics or condensed matter), one can in principle integrate out part of the degrees of freedom so as to attain an effective model ...
0
votes
0answers
16 views

what is a clock state?

Can you tell what is a clock state in atomic physics ? I am reading this paper for a class but I couldn't find the definition of many terms, one of them is the clock state. ...
0
votes
0answers
24 views

Angular momentum wavefunctions with respect to different axes

I've been learning about quantum angular momentum, and I have a question about the relationship between quantum mechanical angular momentum wavefunctions with respect to different axes. I know that ...
0
votes
1answer
17 views

Can a particle accelerator really be constructed which can actually change the properties of a material (create a new kind of atom)?

Can a particle accelerator really be constructed which can actually change the properties of a material (create a new kind of atom)? If not, what are some ways to create or synthesize a new atomic ...
-1
votes
1answer
78 views

What happens in a universe with only two electrons?

What happens in a universe with only two electrons? Do they stay as waves or do they collapse into particles?
0
votes
0answers
13 views

For an entangled state consisting of systems A and B, if A is measured when does the wavefunction at B collapse? [duplicate]

If there are two systems A and B, with an entangled state consisting of $$\mid \psi \rangle = \frac{1}{\sqrt{2}} (\mid \uparrow _A \rangle \,\, \otimes \mid \uparrow _{B} \rangle \,+ \mid \downarrow ...
0
votes
1answer
80 views

Commutator and Hamiltonian

Assume that $[\hat{A},\hat{H}]_-=0$ and $[\hat{B},\hat{H}]_-=0$ but we know that $[\hat{A},\hat{B}]_-\neq 0$. Then there exists degenerate stationary states of $H$. How to prove it?
0
votes
2answers
33 views

Derivation of plane wave from inner product of position ket and momentum ket

In textbooks it seems to be taken for granted that $$\langle \mathbf{r}|\mathbf{k}\rangle = \frac{1}{\sqrt{\Omega}}\exp(i\mathbf{k}\cdot\mathbf{r}).$$ I'm sure it's obvious but is there a ...
0
votes
2answers
39 views

Understanding notation regarding particles states and wavefunctions

In the development in my notes of second quantisation I have a problem in understanding notation. We start by considering a basis $\psi_i(\mathbf{r})$ for the Hilbert space of single particle ...
2
votes
1answer
53 views

Quantum mechanics and Classical limit(s)

I have tried to make sense of this and i am not sure i get it. What i gather from this page about the classical limit is: You need coherent states something like $\hbar \to 0$ is not really enaugh. ...
2
votes
3answers
79 views

Physical meaning of quantum interpretations

Do interpretations of quantum mechanics have physical meaning? An argument for no would be the fact that no matter the interpretation, one gets the same measurements. They also do not follow logical ...
3
votes
1answer
50 views

Can reduced density matrices of sub systems of an entangled composite system be different?

In a 4-dimensional hilbert space, only 4 entangled states( normalized ) are possible ( if I am not wrong ), the bell basis. In each of the state in bell basis the reduced density matrix is ...
3
votes
0answers
22 views

Is there a physical interpretation of Neumann boundary conditions for the free Schrodinger equation on a domain?

Let $\Omega$ be a domain in $\mathbb{R}^n$. Consider the time-independent free Schrodinger equation $\Delta \psi = E\psi$. Solutions subject to Dirichlet boundary conditions can be physically ...
0
votes
1answer
53 views

Can I say that physical entities do not exist and everything is observed “as if” they exist? [on hold]

Maybe it is a bit philosophical question. If I have a model of the universe with all the laws in a computer program. Can I say that the electrons that are modelled in the program exist ? For me it is ...
0
votes
1answer
20 views

Monoatomic fluids and free space around atoms

In monoatomic fluids the atoms can move quite freely around each other. Is there any thermodynamic/statistical mechanic equation how much free space there is between the atoms? This has to be ...
1
vote
0answers
12 views

Classical limit and generalized coherent states

In quantum optics coherent states introduced by Glauber have a localized probability distribution in classical phase-space with maximum following classical equations of motions. This is not a ...
0
votes
0answers
20 views

Measurement of two qubits in a tensor product space

I understand that if we have two qubits, say $\Psi \in \mathcal{H}_1 \bigotimes \mathcal{H}_2$ where Alice has the first qubit, and she makes a measurement and ends up with the state $\phi \in ...
0
votes
0answers
24 views

Physical significance of Cayley Transform

In the book on Quantum Mechanics by Capri (in Chapter 6), its said that an operator $A$ is self adjoint if the operator, $U$ given by $$ U = (A - i I)(A + i I)^{-1} = -(I+iA)(I-iA)^{-1} = -\text ...
-2
votes
0answers
24 views

Time dependent and Time Independent Schrödinger Equation [on hold]

What is the meaning of Schrödinger's Time dependent and Time Independent Equation?
2
votes
3answers
221 views

Normalization problem with hydrogen wavefunction

Suppose you have a mix of states made up of the Hydrogen $\lvert nlm \rangle$ states where one of the coefficients is unknown. For example: $$ \lvert \psi\rangle=A\lvert 100\rangle + ...
0
votes
0answers
19 views

Unitarity of Symmetrisation operators

How can i proove that the symmetrisation operators $S_{\pm}$ are unitary? Defining $S_{\pm}$ on the $N$ Particle Fock Space by it's effect on $|\Psi \rangle=| \Psi_1 \rangle \otimes... \otimes| ...
0
votes
0answers
27 views

Is my window's semi-transparency a consequence of elementary quantum mechanics? [duplicate]

Studying mathematical concepts of quantum mechanics, I have recently become familiar with the classical model of one-dimensional particle being scattered by a potential barrier. As a mathematician, I ...
3
votes
2answers
59 views

Why do we not require higher derivatives to match at boundary when solving the Schrödinger equation in a given potential?

When solving the time independent Schrödinger equation for a given potential in 1D, the main part of the solving involves matching boundary conditions. Usually, we require the value and the first ...
0
votes
1answer
33 views

Question regarding NaCl equilibrium separation

So I am tutoring someone later and one of the problems is from Eisberg/Resnick Ch 12. The potential energy $V$ of NaCl can be described emperically by $$V = \frac{-e^2}{4\pi\epsilon_0 ...
0
votes
0answers
13 views

what does the i-v curve in josephson junction mean?

according to the i-v curve for Josephson junction tunneling for S-I-S (superconductor-insulator-superconductor): do we have any tunneling current for 0< V<= Vc ? if yes, then why don't we show ...
0
votes
0answers
29 views

Rotation of a spin polarization meaning

I've got some quantum state $|s\rangle =\left( \begin{array}{c} cos(\frac {\theta}{2})\\ {e}^{i\phi}sin(\frac {\theta}{2})\end{array} \right)$ I operate on it with a Paul matrix $\sigma_z$ and get a ...
5
votes
0answers
39 views

What is the relation between phase space formulation with Wigner quasi-probability distributions and path integral formulation of quantum mechanics?

I am trying to conceptually connect the two formulations of quantum mechanics. The phase space formulation deals with Wigner quasi-probability distributions on the phase space and the path integral ...
5
votes
0answers
37 views

Why do flux qubits have to be micrometer-sized?

Flux qubits are made using micrometer sized Josephson junctions. They exploit superconducting properties to create and interfere with the magnetic flux between them. My question is that I've seen ...
1
vote
0answers
27 views

Shor's quantum error correction code with unknown basis

$\newcommand{\ket}[1]{\lvert #1 \rangle}$I've met a problem in quantum secret sharing which involves the use of a quantum error-correction code. (let's make it simple to be the 9-qubit Shor code) In ...
0
votes
0answers
20 views

Why must the Gamow state be exponentially increasing?

Why must the Gamow state be exponentially increasing? Why cannot it be exponentially decreasing? The energy is $E- i \Gamma$, but the square root of $E- i \Gamma $ can have either positive or negative ...
1
vote
1answer
67 views

Why is probabilty conserved under time evolution of a system in quantum mechanics?

I've studied quantum mechanics to a certain degree, but one question that I've never been able to get a fully satisfactory answer to is why probability is conserved (by this I mean that it has either ...
1
vote
0answers
41 views

Quantum mechanics question in derivation of Heisenberg-Euler Lagrangian in Schwartz “QFT” notes

In http://isites.harvard.edu/fs/docs/icb.topic1246957.files/IV-9-EffectiveActions.pdf (Page 20) Schwartz derives the Heisenberg-Euler Lagrangian using Schwinger's proper time method. To do so, he ...
2
votes
1answer
37 views

Why is this spin expectation value a vector

I'm given a spin state: $|s\rangle$ = some linear combination of $|\uparrow\rangle + |\downarrow\rangle$ possibly with an imaginary component. $\hat{\mu}_e = g\mu_B\hat{\sigma}$ $g$ is the ...
0
votes
2answers
51 views

How do I operate on a spin state with a sigma operator?

For any arbitrary spin state $|s\rangle$. How do I operate on it with the Pauli spin matrix, $\hat{\sigma_z}$? Does this have something to do with a Bloch sphere?
0
votes
1answer
32 views

Use of termination in solving quantum harmonic oscillator, hydrogen atom etc

I can't seem to understand the use of termination to make the series solutions physically acceptable (when solving the linear harmonic oscillator etc.). So what if the series does not terminate, it's ...
0
votes
1answer
17 views

Polarized Filtering Frequency Shift?

A polarized filter is exposed to a unpolarized light source. The output of the filter should be of lower intensity, hence lower energy. Should not the filtered light be of a lower frequency to ...
0
votes
1answer
29 views

How do I find an expectation value for an electron's magnetic moment?

Given a spin state: $|s\rangle$ = some linear combination of $|\uparrow\rangle + |\downarrow\rangle$ possibly with an imaginary component. How do you get from the definition of a magnetic momentum ...
1
vote
0answers
70 views

What does it mean: “If you scream in Hilbert space, nobody will hear you!” [on hold]

This question may not be appropriate for this site and if it so, sorry for that. Today, I have heard the following quote from one of my friends: If you scream in Hilbert space, nobody will hear ...
6
votes
3answers
437 views

The meaning of the phase in the wave function

I have just started studying QM and I got into some trouble understanding something: Let's say there is a wave function of a particle in a 1D box ($0\leq x\leq a$): $$\psi(x,t=0) = ...
0
votes
1answer
51 views

Why do $S_x$ and $S_y$ flip up/down spin states but $S_z$ does not?

By using the notation $S\lvert s,m_s\rangle$, such that $\bigl\lvert\frac{1}{2},\frac{1}{2}\bigr\rangle=\lvert+\rangle$ and $\bigl\lvert\frac{1}{2},-\frac{1}{2}\bigr\rangle=\lvert-\rangle$ we can ...
1
vote
2answers
48 views

can one distinguish between superposition with randomized phase and classical probability?(an experiment)

I hope that the following experiment will help me understand the topic better. Let's say my friend is sending me photons via two channels and he is doing it in one of the following two ways: he is ...
3
votes
1answer
64 views

Resources for introductory quantum statistical mechanics

I am currently struggling to understand my basic introductory course on quantum statistical mechanics and I have done a basic course on single particle quantum mechanics. I was wondering whether ...
0
votes
0answers
38 views

Summing over quantum states

For a system of $N$ identical particles we deal in quantum mechanics with wave functions $\langle \{\mathbf{r}_i \} \mid \Psi \rangle=\Psi(\mathbf{r}_1,\dots,\mathbf{r}_N)$ from which determine the ...
0
votes
1answer
50 views

Why is the position space free particle wavefunction a function of momentum?

This is one of those little things that has always confused me. If someone said to you "in quantum mechanics, the eigenfunctions of a free particle are $\exp(ipx/\hbar)$" how would you know that ...
6
votes
2answers
271 views

Double slit experiment with animals as observers

I was searching about the double slit experiment, reading and watching videos, etc. If I understood correctly, when they measure the photon it behaves like a particle. On the Youtube video Tom ...
3
votes
1answer
34 views

Necessary and sufficient conditions for a function to be the Wigner function of state

For any quantum state defined with a continuous position, the Wigner function is a quasiprobability distribution on phase space. It has many properties, such as that its marginal are probability ...
0
votes
1answer
37 views

Infinite Energies of a particle in a rectangular box

For a particle trapped inside a rectangular box of side lengths $l_x$ $l_y$ and $l_z$, the energies are ...
-2
votes
1answer
39 views

Spin of a particle (Quantum Mechanics) [duplicate]

Why the intrinsic spin cannot be expressed in terms of polar vectors or the orbital variables $\bf r$ and $\bf p$? Or, why do we need matrix representation for Spin?
1
vote
1answer
47 views

Why is it “disconcerting” if the components of an operator do not commute?

A symmetrized operator is given by $$\hat{R}=\frac{1}{2\hat{H}}\hat{N}+\hat{N}\frac{1}{2\hat{H}}.$$ With $\hat{H}$ the Hamiltonian and $\hat{N}$ the first moment of energy. The defined $\hat{R}$ is ...