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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3
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2answers
199 views

Why do the ladder operators in harmonic oscillators work?

The Hamiltonian can be diagonalized by transforming $x$ and $p$ to $a$ and $a^\dagger$. I understand how one proceeds from there to find the spectrum of $a^\dagger a$, the ground state $|0\rangle$ and ...
0
votes
1answer
19 views

Why characteristics graph of Geiger Muller Counter always goes up?

The characteristics graph of Geiger Muller Counter always keeps going up and does not drop down . It may remain constant over an interval but does not drop down on the graph scale. Why it does not ...
10
votes
1answer
151 views

What is known about the hydrogen atom in $d$ spatial dimensions?

In a first (or second) course on quantum mechanics, everyone learns how to solve the time-independent Schrödinger equation for the energy eigenstates of the hydrogen atom: $$ ...
0
votes
0answers
29 views

Fermi's golden rule and the DoS of scattering states

Can the Fermi's golden rule $$\Gamma_{fi} ~=~ \rho(E_f) \frac{2\pi}{\hbar} |M_{fi}|^2$$ be applied for transitions of discrete states to scattering states? If yes, then what should the density of ...
-2
votes
1answer
103 views

Ground state energy of spin 1 particle

So I have this Hamiltonian for a particle with spin 1: $$ H=aS_{z}^2+\frac{\hbar\omega}{\sqrt2}S_{x}$$ where ($a$ and $\omega$ both real constants): $$ S_{z}=\hbar\begin{pmatrix} 1 & 0 & 0 ...
1
vote
1answer
38 views

Why the constancy of an observable w.r.t time depends on whether it commutes with $H$ or not?

I have been reading Modern Quantum Mechanics by J.J.Sakurai. Under the chapter Quantum Dynamics, the author says if an observable $A$ initially commutes with the Hamiltonian operator $H$, then it ...
0
votes
1answer
21 views

CNOT gate with trapped ions

I'm interested in knowing the structure of a CNOT gate, in quantum computing. THe problem with that is, that I've read how the structure of a nuclear quantum computer works, but I still don't ...
0
votes
0answers
43 views

Why is the Hermitian conjugate of the Fourier transform of an operator not the transform of the Hermitian conjugate? [migrated]

It is defined that: \begin{align} O(\omega)&=\frac{1}{\sqrt{2\pi}}\int O(t)e^{-i\omega t} \mathrm{d}t \tag{1} \\ O^{\dagger}(\omega)&=\frac{1}{\sqrt{2\pi}}\int O^{\dagger}(t)e^{-i\omega t} ...
3
votes
1answer
42 views

Behavior of atom's wave packets in a gas

It is my understanding that the wave packet of a free localized particle spreads with time. My question is what is the best description of the particles in a gas inside a closed container: Do they ...
0
votes
1answer
54 views

Magnetic field induce photons?

So silly question, can a oscillating magnetic field excite electrons around atoms such that they produce photons (In other words can an applied magnetic field increase the energy level of electrons ...
0
votes
0answers
49 views

What knowledge do I need to learn Quantum Physics? [duplicate]

I have a quick question. What prior knowledge do I need to learn and understand quantum physics. For example, what type of math do I need to know, what level of physics, etc.
0
votes
1answer
33 views

How to check if a Hamiltonian is PT symmetric or not?

Consider the Hamiltonian $$H=p^2+ix^3+ix.$$ This paper by Carl M bender claims this is a $PT$ symmetric Hamiltonian. In this he describes $PT$ symmetry as parity $P$, whose effect is to make ...
10
votes
2answers
1k views

Can't quantum teleportation be superluminal some percentage of times?

I apologize if this is a really silly question. In the (textbook) quantum teleportation algorithm, in the step right after Alice has measured her system but before she has sent her classical ...
0
votes
0answers
20 views

Overtone Transition Probability

For an anharmonic potential, like the morse potential, higher order transitions (overtone) with $\Delta n=\pm2,\pm3,..$ are allowed. How do I calculate the probability $P$ for such transitions? My ...
0
votes
1answer
73 views

Propagating a Gaussian wavepacket backwards in time

So, I'm following the MIT OCW lectures on 8.04 quantum mechanics by Prof. Allan Adams. I have the expression for the probability distribution of a gaussian wavepacket for a free particle situation. No ...
0
votes
1answer
37 views

Rate of the increase of width of a Gaussian wavepacket

So, I'm following the MIT OCW lectures on 8.04 quantum mechanics by Prof. Allan Adams. I have the expression for the probability distribution of a gaussian wavepacket for a free particle situation. No ...
3
votes
2answers
117 views

Where are the photons coming from?

Particles and Antiparticles can annihilate, and they are completely destroyed in the process, which creates photons. From wikipedia: ...
-3
votes
2answers
49 views

What makes the probability distribution of a wavefunction in QM intrinsic? [closed]

I know that the usual interpretation of the wavefunction in QM is that it´s associated with a probability distribution of measurable quantities. Not a deterministic probability (like the probabilities ...
12
votes
3answers
2k views

How come light waves don't get caught and absorbed by the electrons of oxygen atoms in the in air?

Shouldn't air be opaque since instead of coming into our eye, the lightwaves get caught in the electrons? If oxygen does absorb light waves, how come air is not hot and you can see through it? The way ...
1
vote
1answer
79 views

How is no-conspiracy theory compatible with determinism? [closed]

Bell's theorem states that any physical theory that incorporates local realism and the no-conspiracy assumption cannot reproduce all the predictions of quantum mechanical theory. Hence, we cannot ...
2
votes
1answer
56 views

Expressing eigenstates of $\mathbf{L}^2$ and $L_z$ in terms of the Cartesian eigenstates $|n_x\, n_y\, n_z\rangle$

I want to express the degenerate eigenstates of the three-dimensional isotropic harmonic oscillator written as eigenstates of $\mathbf{L}^2$ and $L_z$, in terms of the Cartesian eigenstates $|n_x\, ...
2
votes
1answer
33 views

Obtaining wave function from field equation

The Dirac field $\Psi(x)$ satisfies the Dirac equation $$(i\gamma^\mu\partial_\mu-m)\Psi(x)=0$$ When we quantize, each of the four components of the Dirac field becomes an operator that creates or ...
0
votes
0answers
35 views

Rotations acting on quantum states

Suppose I have a free relativistic massive particle described by a state $|p,\sigma\rangle,$, with $p^\mu=(p^0,0,0,p^3)$, so that $P^3|p\rangle=p^3 |p,\sigma\rangle$ and ...
0
votes
2answers
51 views

Can conducting electrons in a metal be modeled at all as classical particles?

I have seen computational models that treat the highest energy electrons in a conducting metal as classical particles in a plasma, the ions being held in place with some sort of heuristic ...
0
votes
0answers
63 views

What does it mean to take a derivative with respect to $\hbar$?

Problem 6.32 of Griffiths Introduction to Quantum Mechanics, 2ed is In part (b), we take a derivative with respect to $\hbar$. Since $\hbar$ is a constant, what does it mean to take a derivative ...
3
votes
2answers
47 views

Introducing a phase, what changes?

This question is related to: Mach-Zehnder interferometer and the Fresnel-Arago laws Let us say we have unpolarised wave taking the form: $$\psi=\psi_0 e^{i(kx-\omega t)+i\phi(t)}$$ Where $\phi$ ...
3
votes
1answer
37 views

Spread of the energy levels and sharp energy eigenvalues of the Schrodinger equation of the H-atom

Solving the Schroedinger equation for the H-atom (or any other system, say a particle in a box, or harmonic oscillator or anything), we obtain the energy eigenvalues are sharp with no spread. However, ...
5
votes
5answers
134 views

What is the explanation for the interference patterns in MWI?

In Young's double-slit experiment, MWI states that in some "worlds" the particle goes through one slit, and in others it goes through the other. If this is so, why do we get an interference pattern? ...
2
votes
0answers
35 views

Is electron phonon interaction important away from fermi surface?

In weak coupling superconductor, the effective electron phonon interaction can be written as $$ H_{eff}=\frac{1}{2}\sum_{q,k_1,k_2,\sigma_1,\sigma_2} V_{k_1,q}C^{\dagger}_{k_1+q,\sigma_1} ...
0
votes
1answer
30 views

Why is the interaction energy of the electrons in an atom positive?

Consider a simple Hamiltonian for the Helium atom (where $e'^2 = e^2/4\pi \epsilon_0)$: ...
46
votes
6answers
5k views

Why does a system try to minimize its total energy?

Why does a system like to minimize its total energy? For example, the total energy of a $H_2$ molecule is smaller than the that of two two isolated hydrogen atoms and that is why two $H$ atoms tries ...
0
votes
0answers
63 views

Feynman lecture - bell's theorem, entanglement

My question regards this video: https://www.youtube.com/watch?v=AyejXtZrGb0 Feynman is illustrating entanglement, bell's theorem etc... using correlated boxes. I take the entangled boxes as ...
0
votes
1answer
44 views

What causes the universe to manifest a given value upon measurement in super-deterministic theory? [closed]

Bell's inequalities show that we have to give up freedom or local realism. If we give up freedom, we have super-determinism, if we give up local realism, we have free-will. In super-deterministic ...
3
votes
0answers
62 views

A question on the Chern number and the winding number?

Let $\mid \psi(x,y) \rangle$ be a normalized wavefunction living in a $d$-dimensional Hilbert space and depend on two real parameters $(x,y)$ that belong to a closed surface (e.g., $S^2, T^2$, ...). ...
0
votes
0answers
50 views

Can nonrelativistic QM, as used in bound states, be derived from QFT? [duplicate]

Nonrelativistic QM can be applied to bound states like a hydrogen atom. QFT is used for free particles (whatever one means by particles) that shortly interact with each other and are free again after ...
-6
votes
1answer
86 views

If E= hv then E= mc2 then h=mc2/v! [closed]

E= pc (1) = hv (2), p= mc (3) From (1) and (2): c= hv/p (4) We put (4) in (3): p=hv/p.m => p2=hvm (5) If we use E=hv in (5) we will get: E= p2/m (6) We use (3) in (6) we will get: E= mc2 From ...
0
votes
1answer
48 views

Finding similar quantum superposition pairs [closed]

I am not sure if my thinking is correct and I'd like to ask if someone can confirm it, or give explanation, what am I doing wrong. I did task where I was asked to tell if pairs of expressions for ...
0
votes
1answer
49 views

Multiplication of associated probabilities

If a state $\psi $ is in the $ S_{z} $ basis represented by $\mid\psi\rangle = c_{+}\mid z\rangle + c_{-} \mid -z\rangle$ Does the associated probabilities change when I multiply $ \psi $ by $ ...
-4
votes
1answer
60 views

Concerning The Oil Drop Experiment: How does ionizing radiation create the electron(s) that the droplets of oil collect?

Concerning the Oil Drop Experiment: I read, “Ionizing radiation is used to create the electron that the droplets of oil collect. When the air in the apparatus is bombarded by this ionizing radiation ...
-1
votes
1answer
46 views

Implications of weak measurement on entanglement

What are the implications of weak-measurement on entangled particles, and how does that resolve the problem of non-superluminal quantum "communication"? If I understand correctly, entangled particles ...
5
votes
2answers
115 views

Is wavefunction collapse “global”?

I have the feeling that the premises of this question may not be coherent (so to speak), but here goes: Suppose we have a system $X$ in a quantum superposition between states $0$ and $1$, say, with ...
1
vote
0answers
30 views

Schrödinger's cat experiment in the context of decoherence

I am trying to visualize in more detail the Schrödinger's cat experiment in the context of decoherence. Please let me know if the description below makes sense or is somehow flawed. If the ...
0
votes
0answers
26 views

Probability density for spinors

I am approaching Relativistic Quantum Mechanics seriously for the first time, going through Bjorken & Drell and doing all the excercises, but I am facing some problems with 3.1. Derive (3.11) ...
2
votes
2answers
139 views

Is my understanding of the delayed choice quantum eraser correct?

I'll say in advance that I am by no means an expert on Quantum Mechanics. I understand the basic mathematics of it (Wave function and Schrodinger equation), but did not go deeply into it or study it ...
0
votes
0answers
64 views

Usage of Complex Numbers in Quantum Mechanics [duplicate]

In Griffiths 2nd Edition Quantum Mechanics page 148, it says when describing the eigenfunction to a part of the central potential problem as $$\mathrm e^{i m \phi}$$ "In electrodynamics we would ...
1
vote
0answers
53 views

Proof for fluctuations in vacuum

I'm not a physicist. My understanding of Heisenberg's uncertainty principle and its proof (that is given by an imaginary microscope) is that for example: at a specified time determining the exact ...
2
votes
0answers
61 views

Gauge transformations for Schrödinger equation [closed]

I want to prove the Schrödinger equation is invariant under the gauge transformations \begin{align*} \mathbf{A} & \rightarrow \mathbf{A}' + \mathbf{\nabla} \chi \\ \phi & \rightarrow \phi' - ...
-2
votes
1answer
45 views

Do we have rest mass according to quantum physics? [closed]

I know wave must be in motion and resonant waves are actually in motion. So I don't understand what is a rest mass of a particle. If a particle is just a wave in a particular field, it should be ...
-3
votes
1answer
75 views

Are one photon at-a-time experiments regarded as the Quantum versions of Classical experiments? [closed]

Is it a correct distinction to regard classical experiments conducted one photon at-a-time as the quantum version of the experiments? For instance, if we take Young's original double-slit, and convert ...
0
votes
1answer
72 views

Why does the equality $\int \mathbf{r}\times \nabla f d\nu=0$ holds? [closed]

My question comes from Problem 4. Classical laws for angular motion of Practical Quantum Mechanics. And the Prob.4 is that, To show that the classical relation between angular momentum ...