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 ...

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Estimate of the second shallowest bound state?

Suppose we have a 1D potential $V(x)$ of finite range, i.e., $$ V(x) ~=~0 $$ for $|x| > b $. The potential might support several bound states. The shallowest one can be infinitesimally small. ...
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13 views

Is uncertainty in velocity via HUP reference frame dependent? [duplicate]

Simply put HUP involves position and momentum, further more consider a mass of 1kg. as momentum is mass X velocity = 1X velocity = velocity for calculation purposes. now for a stationary observer the ...
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1answer
70 views

References for experimental results of the double-slit experiment

Every other popular science book and intro level text on QM starts with the double slit experiment. It is always just stated as a fact that experiments have been done, actual data is never presented ...
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40 views

What is a good book describing the major experiments in Quantum mechanics? [on hold]

I need some book suggestions on few of the major experiments done in Quantum Mechanics which are important in terms of what they imply, how they prove or disprove any theory that still exists or was ...
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35 views

Wave Equation Variables and Interpretation [on hold]

Consider the scalar wave function $\Psi = \exp[i(kr -\omega t)]$, where $k$ is the wave number and $r$ is the spatial coordinate. We can alternately define $k$ to be the wave-vector and $r$ to be ...
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2answers
178 views

How to know if a wave function is physically acceptable solution of a Schrödinger equation?

How does one decide whether a wave function is a physically acceptable solution of the Schrödinger equation? For example: $\tan x$ , $\sin x$, $1/x$, and so on.
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30 views

Symmetry Group of system to a given Hamiltonian

I want to determine the symmetry group of the following system: I consider a charged particle in a spherically symmetric potential $V$ and a homogeneous electric field of magnitude $E$ in ...
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0answers
25 views

Probabilities with a qubit

A two-state quantum system has orthonormal energy eigenstates ψ1 and ψ2, with energy eigenvalues E1 and E2 = E1 + ∆E (∆E > 0). These energy eigenstates form a complete set of wavefunctions for the ...
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3answers
75 views

EPR Paradox resolution: the spin is fixed at creation but its measurement isn't?

The Wikipedia article on the EPR paradox uses the example of an electron and positron created from a common source, each moving in an opposite direction to the other. Detector A is used to measure the ...
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3answers
41 views

Conceptualization and modelling of spin

I'm trying to get a decent understanding of the bell inequality, and so am trying to understand spin both conceptually and mathematically. When I picture spin, I imagine a sphere rotating about its ...
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2answers
54 views

Point-like nature of particle interaction and wave function non-locality

Let us consider the Hamiltonian for the hydrogen atom $$ ...
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15 views

States in valence and conduction band

I often see a Hamiltonian in second quantization written for the valence and conduction band. Now, I was wondering: What are the single-electron states that form the prouct state they act on? So what ...
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12 views

Excitation probability given pulse bandwidth and atom linewidth

Consider photon source producing photon pulses with a frequency distribution $f(\omega)$ and a glass tube filled with a gas. The atoms of the gas can be excited by photons with a frequency of ...
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1answer
94 views

Visualisation of electron

first things first, I'm not by any means a physicist nor a student of physics. I study graphic design. Theme of my bachelor thesis is visualisation of physical and mathematical phenomenons, long story ...
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6answers
2k views

What was the need for doing experiments to prove quantum entanglement?

This question comes from someone who is interested in Physics but with no theoretical background. In 1936, EPR presented the thought experiment which later came to be known and quantum entanglement. ...
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26 views

Cohen Tannoudji solutions to exercises

Does anyone know where to find the solutions to the exercises of Cohen-Tannoudji's Quantum Mechanics? I am gonna try to do all of them and would like to check.
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2answers
41 views

What role does the Higgs Field play in the universe?

The Higgs field is known as a physical field that covers the entire universe, giving particles their mass. However, that got me thinking if the Higgs field not only gives mass to other particles, but ...
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2answers
90 views

Separability of a Hilbert space and its implications for the formalism of QM

In the text I'm using for QM, one of the properties listed for Hilbert space that is a mystery to me is the property that it is separable. Quoted from text (N. Zettili: Quantum Mechanics: Concepts and ...
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1answer
27 views

Restrictions on Bell-type inequalities

While deriving and proving Bell-type inequalities of the form $|E(a,b)-E(a,b')|+|E(a',b)+E(a',b')|\leq 2$ I know that the conditions on the operators $O_a$ and $O_b$ are that they must be bounded ...
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2answers
61 views

Why doesn't the electron lose or absorb energy while remaining in a selected orbit?

Postulate 2: When an electron revolves in any selected orbits, it neither emits nor absorbs energy . The energy of an electron in a particular orbit remains constant. Thus, Bohr, by postulating ...
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17 views

Quantum harmonic oscillator doughnut shape

When phase-space trajectory is plotted for classical harmonic oscillator for p(t)=mx0ωcos(ωt +δ0), a circle is obtained. When done same for the quantum harmonic oscillator, why do we get a doughnut ...
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2answers
71 views

How to handle the potential $V(x)$ or $V(\phi)$ which is not analytic in QM and QFT

In QM, $$\hat{x}\phi(p)=i\frac{\partial}{\partial p} \phi(p)$$ and when $V(x)$ is an analytic function of $x$, then $$V(\hat{x})\phi(p)=V(i\frac{\partial}{\partial p} )\phi(p)$$ and we can do Taylor ...
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28 views

How to derive a new form of Hamiltonian operator in quantum mechanics using canonical commutation relation?

How does one derive $$\hat{H} = \frac{1}{2}\hat{p}^2m(\hat{q}) - \frac{i}{2}\hat{p}\frac{m'(\hat{q})}{m^2(\hat{q})} + V(\hat{q})$$ from hamiltonian $$\hat{H} = \hat{p}\frac{1}{2m(\hat{q})}\hat{p} + ...
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1answer
46 views

Energy in harmonic oscillator [on hold]

The expectation value of the potential energy is exactly half the total according to Griffiths. Is that case always true for quantum harmonic oscillator? Is that the case also for classical harmonic ...
3
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1answer
113 views

1D Finite potential well: solutions with $\sinh$ and $\cosh$?

So I am studying the (one dimensional) quantum mechanical finite potential well defined by: $$ V(x) = \cases{0, &|x|>a\cr -V_0, &|x|<a} $$ where $V_0>0$ is a real number. I know ...
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1answer
40 views

Do entangled particles lose entanglement after polarizing filters?

If two entangled particles are sent through different polarizing filters, do they lose their entanglement after the filters?
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1answer
52 views

Does Bell's inequalities also rule out non-computable local hidden variable theories?

I have beenn reading different articles on Bell's assumptions and interpretations, including superdeterminsm. I always end up dizzy when I try tho think about this specific question, so any hints ...
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2answers
61 views

Collapse of the wave function and Heisenberg uncertainty

I have been studying quantum mechanics for a few weeks, in particular wave mechanics, as created by Schrodinger, and his equation. As a high school student, I haven't found an answer to this question ...
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1answer
111 views

Deriving a Useful Solution of the Schrödinger Equation [on hold]

How does one derive the fact that $$\psi(t,x) = (\tfrac{2 \pi \hbar t}{m})^{-d/2}\int_{\mathbb{R}^d} e^{im\tfrac{(x-y)^2}{2\hbar t}}\psi_0(y)dy$$ is a solution of the time-dependent Schrödinger ...
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1answer
33 views

Eigenvalues of Angular Momentum in Quantum Mechanics

The eigenvalue equation of the $L^2$ operator is given by $$L^2f_l^m = \hbar ^2l(l+1)f_l^m$$ Side: So a determinate state for some observable $Q$ is a state where every measurement of $Q$ returns ...
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0answers
237 views

Why discrepancies in the Schrödinger equation? [duplicate]

Why is there seemingly two definitions of the Schrödinger equation? \begin{equation} i\hbar\frac{\partial}{\partial t}\Psi=\hat H\Psi. \end{equation} And \begin{equation} i\hbar ...
3
votes
2answers
77 views

Importance of Kronecker product in quantum computation

To get product state of two states $|\phi \rangle$ and $|\psi \rangle$, we use Kronecker product $|\phi \rangle \otimes |\psi \rangle$. Instead of Kronecker product $\otimes$, can we use Cartesian ...
4
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3answers
106 views

Why every state evolving infinite time becomes the ground state in QFT?

For any state $|\phi \rangle $ evolving infinite time $$\lim\limits_{t\rightarrow \infty} e^{-iHt}|\phi\rangle=\lim\limits_{t\rightarrow \infty} e^{-iHt}|n\rangle\langle n|\phi\rangle$$ Let ...
2
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0answers
24 views

With what fraction photon quanta emission rate is decreased in the expanding universe? [on hold]

Light from edge of the observable universe has travelled 13.8 billion light years so far. And, that edge itself has travelled 32.2-33.2 billion light years (that's why actual radius of observable ...
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0answers
40 views

Allowed Values of Angular Momentum for a Rotating Mass

I am attempting to calculate all possible values of angular momentum, $L_z$, which can be found by making a measurement on the following system: A small mass, $M$, is attached to the end of a rigid, ...
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0answers
46 views

how to prove the following equations? [on hold]

Equations in this image include some confusing steps for me, I tried but no results came out. please if some one can solve it I'll be very thankful.
3
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1answer
49 views

Quasiclassical QM for central fields

Let's have quasiclassical QM for central field $V(r)$. The Schroedinger equation for radial part of wavefunction $R_{nl}$ after substitution $u_{nl} = rR_{nl}$ takes the form $$ u_{nl}{''} + ...
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3answers
76 views

State vector vs density operator

We formulate quantum mechanics using language of state vectors. One alternative formulation is possible using density operator or density matrix. Why we are doing this alternative approach? Is the ...
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2answers
78 views

What is the most agreed upon quantum mechanical equation of motion?

On multiple Wikipedia articles, it mentions several quantum mechanical equations of motion, namely those by Schrödinger and Heisenberg. Which one is the most accurate and agreed upon quantum ...
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0answers
15 views

Antiunitary operator, momentum operator [on hold]

Assuming the time-reversal operator $T$ $T|x>=|x>$ Now I want to calculate $TpT^{-1}$ So, $TpT{-1}|x>=Tp|x>=\int\int T|x'><x'|p|p'><p'|x>=\int\int ...
1
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1answer
73 views

Eigenvalues of hamiltonian [on hold]

Q: THe hamiltonian which describes the motion of a particle in an one dimensional potential V(x) is $H_0=\frac{p^2}{2m}+V(x)$ , where $p=-i\hbar \frac{d}{dx}$ is the momentum operator. $E_n^0$ , ...
27
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3answers
2k views

What do we see while watching light? Waves or particles?

I'm trying to understand quantum physics. I'm pretty familiar with it but I can't decide what counts as observing to cause particle behave (at least when it's about lights). So the question is what do ...
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2answers
45 views

Can Quantum Entanglement and Quantum Superposition be considered the same phenomenon?

Quantum entanglement is known to be the exchange of quantum information between two particles at a distance, while quantum superposition is known to be the uncertainty of a particle (or particles) ...
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2answers
57 views

Creation and annihilation operators in Hamiltonian

If I find a Hamiltonian $H = \sum_{k} \varepsilon_k a_k^{\dagger} a_k + \sum_k V_k a_k^{\dagger} a_k$ then I was wondering: As far as I know this is many body theory and so these operators act on ...
4
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0answers
280 views
+250

Horrifying electron gas model

I am given the Hamiltonian, in an exercise called plasmons, and where $\langle, \rangle $ denotes the expectation value. $$ H = \sum_{k} \varepsilon_k a_k^{\dagger} a_k + \sum_{k_1,k_2,q} V_q ...
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0answers
32 views

Larmor Precession of a macroscopic number of electrons

I know that there are some similiar questions out there, but I'm still quite puzzled by the following problem. Say i have a box full of interacting electrons ( I'm not sure if it would change anything ...
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0answers
42 views

Interpretation of all eight solutions of the Dirac equation

There are eight solutions of the Dirac equation. $u_1, u_2, u_3 , u_4$ and $v_1,v_2,v_3,v_4$. Conventionally the four solutions ($u_3 , u_4,v_3,v_4$.) following from $E=- \sqrt{ (\vec p)^2 +m^2}$ are ...
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0answers
46 views

What is really interacting in weak interactions?

Only particles with chirality $-1$ do interact weakly. The corresponding eigenstate in the Dirac basis is $ \Psi_L = \begin{pmatrix}f \\ -f \end{pmatrix} = \begin{pmatrix}u_r {\mathrm{e}}^{-imt} \\ ...
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44 views

Please help with quantum mechanics [closed]

Let the Hamiltonian of two nonidentical spin 1/2 particles be where and are constants having the dimensions of energy. Find the energy levels and their degeneracies.
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1answer
39 views

Wave packets and half-width at half-maximum

Suppose we have a Gaussian wave function and amplitude distribution function $$\psi(x) = (\frac{2}{\pi a^{2}})^{1/4}e^{-x^{2}/a^{2}}e^{ik_{0}x}, \qquad \phi(k) = (\frac{a^{2}}{2\pi})^{1/4}e^{-a^{2} ...