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.

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30 views

Interpretation of creation and annihilation operators acting in the state of a interacting system

If I have a system of $N$ non-interacting fermions, I can write the wave function of the ground-state of the system using a Slater determinant $$ \Phi_{0}(\textbf{r}_{1}, ..., \textbf{r}_{N}) = \frac{...
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3answers
85 views

Is $X\otimes X$ not the simultaneous position operator?

I had thought that $X\otimes X$ would be the operator on $H_1\otimes H_2$ to simultaneously measure the x-positions of two particles. But there seems to be something wrong with this -- for a given ...
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1answer
38 views

What are the conditions for nuclear decay?

I read something about that the Q-Value hast to be greater then $0$. But there must be certainly more conditions otherwise there would be nuclei that could't decay.
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49 views

What was the origin of Bohr-Sommerfeld's quantization rules?

What made Bohr and Sommerfeld think momentum and angular momentum is quantized? What is the meaning of momentum quantization in harmonic oscillator? Can we imagine it (by some classical example)?
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30 views

What level of quantum mechanics is needed for theoretical particle physics? [closed]

I've taken an introductory course on Quantum Mechanics which focused on the wave mechanics side of things. Sometimes my professor would use Dirac notation, but not strictly. I have a lose grip on that ...
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1answer
125 views

Representing quaternionic algebra with creation and annihilation operators?

The paper "Quantized Grassmann variables and unified theories" says given creation and annihilation operators $b$ and $b^\dagger$ one can represent quaternionic imaginary units $q_1$, $q_2$ and $q_3$ ...
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18 views

Difference between coherent and incoherent energy transfer (e.g. in photosynthesis)?

Several authors distinguish between incoherent and coherent when describing the energy transfer mechanism that forms the basis for photosynthesis. (e.g. Clegg & Sener 2010 and Keren & Paltiel ...
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5answers
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What is temperature on a quantum level?

When I was in high school, I learned that temperature is kinetic energy. When I learned statistical physics, we learned that temperature is a statistical thing, and there was a formula for it. ...
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20 views

Relative phase of a qubit

Is it possible to choose a suitable basis for a qubit so that the relative phase can be changed arbitrarily? In other words, do there exist rotation operators that can take a qubit with a specific ...
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1answer
55 views

Finding the quadrature variance of a superposition of squeezed coherent states

How do you find the quadrature variance of a state $$\lvert x\rangle =\lvert a,b\rangle +\lvert a,-b\rangle$$ where $\lvert a,b\rangle = D(a) S(b) \lvert 0\rangle$? $\lvert x\rangle$ is a ...
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37 views

Basis representation of $F(\hat{X}, \hat{P},..)$

Suppose I know the position or momentum basis representation $X$ of some operator $\hat{X}$ acting on the ket space. Likewise of $\hat{P}, \hat{A}, \hat{B}, ...$ Is the basis representation of $F(\...
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47 views

Liquid Helium as a photocathode?

Photocathodes are usually solid state materials that are hit with (typically pulsed) light to give off electrons to be used for various particle physics purposes. One characteristic (among many) of ...
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28 views

Does pseudospin break the crystal symmetry?

Pseudospin is a concept to describe a superposition of two quantum states. Sometimes, I see a pseudospin texture in the momentum space which breaks a crystal symmetry. A simple example is the ...
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26 views

Tight Binding Hamiltonian for graphene

The TB Hamiltonian for the tetragonal lattice is $ \hat H_0 = -J\sum_{m,n} (\hat a_{m+1,n}^\dagger \hat a_{m,n}+\hat a_{m,n}^\dagger \hat a_{m,n+1}+h.c.) $ How can this be derived for the hexagonal ...
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61 views

Physicist path integral and cylinder set measures

Path integral via discretization So let me start with what seems to be the point of view of physicists (corrections are highly appreciated since this is what I understood!). Let a quantum system with ...
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2answers
53 views

Why are entanglement and purity non-linear functions of $\rho$?

Any linear function of the density matrix can be related to a proper observable, but is it not the case of entanglement and purity?
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1answer
24 views

Heisenberg Hamiltonian 2-Spin Terms in Matrix Representation

I am stuck on the interpretation/derivation of the 2-spin terms of the quantum Heisenberg model Hamiltonian. In this model, our electrons, with spin up or down, are confined to sites on a lattice. ...
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34 views

Stationary State of Quantum Mechanics [duplicate]

Why for every normalized solution to the time-independent Schrödinger equation $E$ must exceed the minimum value of $V(x)$?
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0answers
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Is the Hamiltonian represented as a matrix, in the exponential form of the time evolution unitary operator? [closed]

If yes, what kind of matrix does the hamiltonian represent? Btw the equation I am referring to is 𝑈=𝑒^iHt
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3answers
114 views

Can gravitational waves be used to investigate the inside of black holes?

I do understand that nothing, no particles and no information can escape a BH. Gravitational waves are real, they have been observed. Gravitational waves are disturbances in the curvature of ...
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1answer
91 views

Momentum Wave Function gives strange expectation values

Suppose there's a particle with the wave function $\psi(x)=\frac{1}{\sqrt{L}}$ for $0<x <L$ and 0 everywhere else. One way to get the associated Momentum Wave function is direct integration on ...
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0answers
26 views

Is this solution correct? I do not think it is because the product rule has not been applied to the second derivative wrt to x [closed]

Is this solution correct? I do not think it is because the product rule has not been applied to the second derivative wrt to x.
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32 views

Two definitions of current operator $J$ equivalent?

I am currently reading David Tong's lecture note on quantum Hall effect. In this note, the current operator $\mathbf J$ is defined in two ways: We define $J= -e\dot{\mathbf x}= (-e/m)(\mathbf p+e\...
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Is there a minimum energy in the ground state of a particle in a finite square potential well? If yes then how to find it? [closed]

The equation can be given as: $\phi(x)=Ae^{\gamma x}$ for $x<-\frac {L} {2}$ $$\phi(x)=A \frac{e^{-\frac { \gamma L} {2}}}{\cos\left(\frac{kL}{2}\right)}\cos (kx)$$ for -$\frac {L}{2}<x< \...
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2answers
49 views

Understanding wave function graph

I found this graph from the internet that interprets the graphical representation of wave function.I completely understand the wave function that is depicted by blue line but i really am confused ...
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2answers
91 views

Interpretation of density matrix

In Landau’s Statistical Physics (part 1) , section 5, he writes:" In particular, it would be quite incorrect to suppose that the description by means of the density matrix signifies that the subsystem ...
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1answer
66 views

Understanding the quantum mechanical state vector

According to Griffiths, there is a general state vector $|s(t)\rangle$ that encodes the state of the system. He also says that we take $\Psi(x, \ t) \ = \ \langle x | s(t) \rangle$. Would then mean ...
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3answers
76 views

Is the concept of superpositions saying that the electron is actually in many states?

Basically when I read about it, yes. But I don't completely get why. Let me explain: If I throw a ball into a room and don't look, I would surely say that the ball is at one point in this room. Maybe ...
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16 views

Saturability problem about the quantum Cramer-Rao bound for the multi-parameter quantum metrology

I was studying the multi-parameter quantum metrology these days. And I was confused about the saturability of the quantum Cramer-Rao bound for the multiparameter problem. If all of the generators are ...
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1answer
31 views

Effect of different reference frame on quantum entanglement measurement

According to what I read about entanglement, when you measure the spin of one of the entangled particles all the possibilities collapse to one value immediately and the other particle will give the ...
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0answers
21 views

Non-Markovian noise coupled to atomic system

I want to calculate the density matrix element's average over all the realization of Gaussian colored noise when the atomic system is coupled to the said noise. I know how to do it for atomic energy ...
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1answer
74 views

States for derivatives of wave function?

Given a wave function $\psi_t(x)$. The quantum state of a system at time t can be written as the sum of basis states multiplied by the amplitude: $$|t\rangle = \int \psi_t(x)|x\rangle dx^3$$ What ...
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35 views

How to know if an operator is a Hermitian operator? [closed]

An operator is hermitian if $A=A^H$ but how can i prove that $-\iota\hbar\frac{d}{dx}$ is a hermitian operator and $\frac{d}{dx}$ is a skew-hermitian.
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2answers
54 views

Do gravitational waves disperse/refract (like EM waves in a prism)?

I have read this question: What is the relationship between a gravitational wave and a graviton? where kingledion says: Gravitational waves were theorized a century ago and recently ...
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1answer
32 views

Does this wave function from Zettili book (Quantum Mechanics) violate uncertainy principle?

I am not sure whether my question counts as homework and exercises or not, because I already know the answer. The problem is, I find Zettili answer rather unsatisfactory. Problem 1.11 (a) Find the ...
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1answer
49 views

$s$-parameterized operator-valued Dirac delta function

So I am reading the book named 'Quantum Optics An Introduction' by Werner Vogel, Dirk-Gunnar Welsch, Sascha Wallentowitz and in the section 'Phase-space representations', I struggle to follow one step ...
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3answers
98 views

Can there be interference between a proton and an electron?

For example, we know that we can interfere two different electrons or two different protons by employing them in a double-slit experiment. Now suppose, we mix protons and electrons and shoot them ...
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0answers
57 views

Hawking temperature, uncertainty principle and size of a black hole

I was playing with the Hawking temperature formula $$T_H = \frac{\hbar\ c^3}{8 \pi\ G\ M\ k_B}$$ and I thought it would be interesting to associate a velocity to this temperature: $$k_B\ T_H = \frac{1}...
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0answers
21 views

The stark effect of Hydrogen

I have read the stark effect of Hydrogen (calculating energy levels of the n=2 states of a Hydrogen atom placed in an external uniform electric field along the positive z-direction) from Quantum ...
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31 views

Simple Quantum Eraser

I am familiar with the standard Quantum Eraser experiment. I was thinking of the following. My hunch is that the screen will show an interference pattern since the which way information for the ...
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1answer
62 views

Proof that rotational symmetric potential operators are scalar operators

Defintion: A scalar operator B is an operator on a ket space that transforms under rotations \begin{equation}\left| \xi ' \right >=\exp{(\frac{i}{h} \mathbf{\phi \cdot J})}\left| \xi \right >\...
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2answers
71 views

Hard boundary of Heisenberg's uncertainty principle

Heisenberg's uncertainty principle states that we cannot know the position and momentum of subatomic particles simultaneously...but what exactly is the boundary of size of such a particle? Does such a ...
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0answers
10 views

How to construct general multiparticle states that respect fermionic or bosonic symmetry?

Background: The arena is fixed particle number nonrelativistic quantum mechanics. The state space is $$ \mathbf{H}(1)=\mathcal H\otimes\mathcal S, $$ where $\mathcal H$ is an "orbital" state space ($L^...
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Exchange statistics from topology of configuration space

I'm trying to understand Leinaas and Myrheim's famous 1976 argument for exchange symmetry of the wavefunction. If we consider the configuration space $\mathcal{M}_2$ for two identical particles ...
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7 views

Magnetic susceptibility for particle on a ring

I consider particle on a ring in magnetic field. The presence of magnetic field shifts the particle momentum and I understand to find magnetic flux through the ring. Then, how can I find the ...
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1answer
52 views

Scalar product of eigenstates of $\hat{S}_z$ and $\hat{S}_x$ operators

Suppose that $|s_z\rangle$ and $|s_x\rangle$ are eigenvectors of operators $\hat{S}_z$ and $\hat{S}_x$ correspondingly, with $s_z$ and $s_x$ being eigenvalues. Is there a known formula for the scalar ...
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1answer
77 views

Different formula to find $2\times 2$ Hamiltonian's eigenvalues [closed]

Consider the Hamiltonian $$ \left[ \begin{matrix} E_1 & -A\\ -A& E_2\\ \end{matrix} \right] $$ where $A$, $E_1,E_2$ are real numbers. I have seen a different formula to ...
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1answer
31 views

What is the unit of the current in a square barrier model?

In Quantum Mechanics textbooks, the equation for a electron tunneling through a barrier is $$-\frac{\hbar ^{2}}{2m}\frac{d^{2}}{dx^{2}}\psi \left( x\right) +U\psi \left(x\right) =E\psi \left( x\right)...
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2answers
120 views

Is $[A,\exp{B}]=0 \Rightarrow [A,B]=0$ true?

The backward direction is trivial and this one probably too, but I just can't find a convincing argument. $A$, $B$ are Operators on a Hilbert Space (Ket Space).
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A doubt on waves

We know that every progressive wave depends on its position X and time variable T. y= Asin (kx- wt) My doubt is "Even an election is a wave (de broglie's hypothesis), but we cannot write its equation ...