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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1answer
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Inconsistency in the delta potential

I encountered an inconsistency in the one-dimensional delta potential. Suppose we have a one-dimensional infinitely deep square well from $-L$ to $+L$. We know the eigenstates are sine and cosine ...
0
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1answer
29 views

Few particle fermion system wavefuction

Suppose I have 3 fermions($\left|\psi_1\right\rangle$, $\left|\psi_2\right\rangle$, $\left|\psi_3\right\rangle$) and a system with 3 states ( $\left|1\right\rangle$, $\left|2\right\rangle$, ...
0
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0answers
22 views

Dynamics of modifing a Hamiltonian

I am working on quantum mechanics right now, and I am wondering if there is a qualitative way to think about off diagonal term of a Hamiltonian matrix? I know that we can diagonalize a matrix, then ...
1
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0answers
10 views

Local unitary transformation that maximizes overlap

Could anyone point me in the right direction (reference to papers would suffice) regarding the following: Given two quantum states $|\psi\rangle ,|\phi\rangle \in (\mathbb{C}^d)^{\otimes n}$, where ...
1
vote
1answer
20 views

How can we tell if a molecule is in thermodynamic equilibrium from scattering data?

We have a molecule that is emitting/absorbing photons. We know the Hamiltonian and that there are several levels. We count the emitted photons at different angles and frequencies. We can also do ...
-3
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1answer
68 views

Why do we believe in a “force” driven universe? [on hold]

Why do we not believe in the potential for a "unified force field" universe, to the exclusion of the belief in the potential for a mechanical, gear driven universe, if the correct shape for the gear ...
1
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0answers
38 views

Is Ballentine's description of the Berry phase (in his book _Quantum Mechanics_) flawed?

Ok, so I'm looking at Ballentine's Quantum Mechanics right now, 7th reprint (2010). On page 363, he starts with 12.7 Adiabatic Approximation and quickly moves on to explain Berry's phase on page 365. ...
0
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0answers
39 views

Quantum decoherence and Schrodinger's equation

In non-relativistic quantum mechanics, the equation of evolution of the quantum state is given by Schrodinger's equation and measurement of a state of particle is itself a physical process. Thus, ...
0
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2answers
36 views

Number of Orbitals - Hydrogen Orbital just one, but why can we plot also higher states e.g. SPDF orbits?

I am confused, hydrogen just has one electron in the 1s orbit. but why can we plot all kind of orbitals (higher energy eigenstates for that atom)? My assumption: So physically spoken these orbits ...
0
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0answers
26 views

Wannier Hamiltonian in Momentum Space

In connection to a previous question, We can write the one-particle Hamiltonian in the Wannier basis working on a general vector $v$ as : $$ \langle\vec{R},\,\lambda|\hat{H}|v\rangle = ...
0
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1answer
27 views

Correlation between Bohr-model and quantum physics

If you're looking at the probability of finding the electron of a hydrogen atom at a distance $r$ from the nucleus, it turns out that the Bohr model for the radius of the orbit only correlates with ...
-2
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0answers
65 views

A new interpretation of QM [on hold]

Do you think that this new interpretation of quantum mechanics has solved the measurement problem completely as it claims? http://article.sapub.org/10.5923.j.ijtmp.20140405.04.html
10
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5answers
2k views

How can one derive Schrödinger equation?

The Schrödinger equation is the basis to understanding quantum mechanics, but how can one derive it? I asked my instructor but he told me that it came from the experience of Schrödinger and his ...
0
votes
0answers
26 views

Interpretation of angular momentum in semi-classical vector model

My Professor said that when we calculate the total angular momentum of multiparticles, in this case i.e. 2 particles, we can add total angular momentum by thinking this way, if both spins allign they ...
0
votes
1answer
49 views

Finding the spectrum of a curious hamiltonian

I wish to analyse the following hamiltonian, i.e. find its eigenvalues and eigenstates. $$H = \frac{1}{2}\epsilon(\sigma _z \otimes \mathbb{1} + 1\otimes \sigma _z) - \Delta (\sigma _x \otimes \sigma ...
3
votes
2answers
190 views

1D Infinite Square Box Discrete Energy levels but Continous Momenta?

In the 1d particle in the box the energy of the particle should be completely determined by the momentum of the particle that you observe correct? So how can you have discrete energy levels and a ...
0
votes
1answer
29 views

Example of a state which is positive but its partial transpose is not positive

Could any one give me an example of a state whose density matrix is positive semidefinnite but partial transpose is not positive semidefinnite?
0
votes
0answers
80 views

Momentum operator in Dirac formalism

Could you derive the momentum operator as follows: Since $\mathcal{T}(\Delta x)=\exp(-ip_{x} \Delta x/ \hslash)$, if we set $\Delta x=x-0$ then it follows that $\left \langle x\right | ...
3
votes
1answer
68 views

Where does the partial derivative come from in Sakurai's derivation of the momentum operator?

How is the momentum operator derived in Dirac formalism? I am reading Quantum Mechanics by Sakurai and he gives the following derivation. But I don't understand how he goes from the third equation to ...
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0answers
44 views

Wannier Functions as Discrete Basis

In solid state physics, using Bloch's theorem we know that the one-electron energy eigen-function can be written as $\psi_{\lambda,\vec{k}}(\vec{r})$ where $\lambda$ indexes eigenvalues of $\hat{H}$ ...
2
votes
2answers
103 views

Why do electrons orbit protons? [duplicate]

I was wondering why electrons orbited protons rather than protons orbiting electrons. My first thought was that it was due to the small amount of gravitational attraction between them that would ...
0
votes
0answers
40 views

Bell's inequality

For a project, I'm planning to study Bell's inequality, which as far as I can gather is taken to rule out hidden variable theories of QM. I'm looking for recommendations of decent sources which derive ...
0
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1answer
46 views

Diffraction to be explained without Huygens principle

Can we explain diffraction without using Huygens principle?
0
votes
1answer
28 views

Potential energy given to an electron in a time-varying electric field

Given a general electric field $\epsilon(t) $ directed in the z direction, how would we calculate the potential energy given to an electron as a result of this field?
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0answers
34 views
+100

Wavefunction of isomers

In quantum chemistry, the wavefunction for a molecule can be viewed as the output of a function $\xi(m, n_1,..., n_k)$ with $m, n_i \in \mathbb{Z}^+$ that returns a $|\psi\rangle$ that satisfies a ...
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0answers
52 views

Probability of spontaneous combustion [on hold]

Given the random background quantum noise, what is the probability that it will happen to concentrate in a particular location with sufficient quantity to cause a human being to spontaneously combust? ...
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0answers
73 views

Possible theory of everything? [on hold]

Tell me if there is anything that sounds immediately incorrect about this possibility or if it's already been considered. We know that the universe can be in infinite different quantum states, but we ...
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0answers
35 views

Is this essay topic relating to my level of quantum physics? [on hold]

I am studying mathematics with a minor in physics. My mathematical skills therefore exceed my physics skills, and I have no much trouble with more advanced mathematical techniques. In our current ...
1
vote
1answer
36 views

Defining creation and annihilation operators

Creation and annihilation operators can be defined in several different ways, some more general than others. We usually choose to denote by $a$ the annihilation operator and by $a^\dagger$ the ...
6
votes
2answers
582 views

How is antimatter made?

How is antimatter made in laboratory? Can anyone explain, at the particle level, specifically how anti-protons and anti-electrons are made?
0
votes
0answers
60 views

About the meaning of quantum numbers [on hold]

could someone elaborate the idea of quantum numbers: Azimuthal quantum number (ℓ) Magnetic quantum number (m) Spin quantum number (s) I want to know: their physical meaning and the origin of ...
1
vote
0answers
60 views

Chaotic behaviour re-obtained in QM

In classical mechanics, when we talk about chaotic systems (e.g. double pendulum), we always associate (or justify) them with the non-linearity(and non-integrability) of the differential equations ...
1
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0answers
41 views

Time evolution operator of a periodic Hamiltonian

Suppose we have a Hamiltonian $H(t)$ with periodicity $T$. The time evolution operator in a full period is $$U_1=\cal{T}e^{-i\int_0^T H(t)\mathrm{d}t}$$, where $\cal{T}$ is time ordering operator; ...
1
vote
2answers
96 views

How to understand “always create before we annihilate, not the other way around”?

On the book QFT in a Nutshell by A.Zee page 61 writes Always create before we annihilate, not the other way around. —Anonymous But in this Phys.SE question we are doing it the other way ...
7
votes
1answer
169 views

Why is there $1/2\pi$ in $\int\frac{dp}{2\pi}|p\rangle\langle p|$?

I'm reading Richard MacKenzie's lectures on path integrals and on page 7 he derives the propagator for the free particle as follows: $$ \begin{align} K &= \langle q'|e^{-iHT}|q\rangle \\ &= ...
3
votes
1answer
103 views

Can quantum mechanics be formulated without any reference to pictures?

NOTE: in the following with the word "picture" I refer to Schroedinger, Heisenberg, Interaction pictures, i.e. to the way the time-evolution is "distributed" between states and operators. We often ...
5
votes
1answer
89 views

Hydrogen energy levels and energy-time uncertainty principle

Some hydrogen atom exists in some excited quantum state, and after some time $\Delta t$ it's de-excited, emitting a photon carrying the energy difference. It is claimed that this photon will carry ...
2
votes
0answers
22 views

Detailed Balance for Quantum Master Equations from System Hamiltonians with Degenerate Spectrum

Kossakowski, Andrzej, et al. ("Quantum detailed balance and KMS condition." Communications in Mathematical Physics 57.2 (1977): 97-110) gave a proof that the stationary state of a quantum dynamical ...
1
vote
1answer
33 views

Why does an external laser drive only couples certain levels?

I was always wondering how is it that all the quantum optics levels schemes are depicted as if the laser couples only two certain levels with some frequency. For exmaple the standard lambda system ...
2
votes
1answer
81 views

Linear vs. quadratic dispersion relation

In wave mechanics the dispersion relation between frequency $\omega$ and wave number $k$ is linear: $$\omega_n=c k_n$$ But in quantum mechanics, based on Schrödinger's equation, one can show that we ...
0
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0answers
26 views

Flip of polarisation of light

Consider an optical experiment with photons or light pulses. Is there an optical element that acts in the polarisation degree of freedom like the unitary $$ U = \frac 1 {\sqrt 2} \begin{pmatrix} 1 ...
1
vote
0answers
36 views

A driven quantum harmonic oscillator (DQHO) [on hold]

I'm trying to find the dispersion relation for the DQHO with Lagrangian $$ L(q,\dot q,t)=\frac{1}{2}\dot{q}^2-\frac{1}{2}\omega q^2+F(t)q $$ with $F(t)$ being non-zero for $0<t<T$. The ...
7
votes
3answers
671 views

Mathematical understanding of Quantum Mechanics

Assuming that $\phi(r) = F (\psi(r))$ for some operator $F$ in Quantum Mechanics. Then, in our lecture today, we said that $$\phi(r) = \langle r|F |\psi\rangle = \int_{\mathbb{R}} \langle r |F| r' ...
2
votes
1answer
93 views

Mirror that flips polarisation?

Is it possible to build a mirror which not just reflects a photon but also flips its polarisation from horizontal tho vertical (or vice versa)? The reason why I ask is the following: If I put an ...
0
votes
0answers
33 views

A confusion about the proof of $\hat{p}|x\rangle=i\hbar\frac{\partial}{\partial x}|x\rangle,$ using $[\hat{x},\hat{p}]=i\hbar~?$ [duplicate]

How to prove $$\hat{p}|x\rangle=i\hbar\frac{\partial}{\partial x}|x\rangle,$$ using $$[\hat{x},\hat{p}]=i\hbar~?$$ The question seems to be uncomplete because for any $f(x)$ ...
1
vote
1answer
22 views

Constructing matrix for spin in Stern-Gerlach experiment for arbitrary angle

This is a conceptual question about a problem in Sakurai. I understand how to solve the problem, but there's something about it that irks me, and it feels like I'm missing something. In the problem, ...
6
votes
2answers
80 views

Classical logic in concern with QM Mathematics

In no way am I a physicist, so please excuse improperly used terms. It is in my understanding that Quantum Physics does not obey Classical Logic, hence the existence of Quantum Logic. My questions ...
0
votes
2answers
30 views

Finding out time $t$ when a particle is more likely to be on the right half than the left half of the box [closed]

Question: A particle with mass $m$ is trapped in a box of length $L$. At $t=0$, it has wavefunction as following: $$\psi(x,t=0)=\sqrt[]{\frac2{41\pi}}(3u_1(x)+4u_2(x))$$ where $u_1(x)$ and ...
1
vote
1answer
46 views

Energy Dispersion in Young's Double Slit Experiment

In Young's double slit experiment, when you see the diffraction pattern, why does the intensity of the light fade out as you move from the central maximum? I think it has something to do with the ...
0
votes
1answer
59 views

Can the simulation argument be ruled out? [closed]

I am neither a physicist nor a mathematician - simply an interested beholder of the current situation interested in quantum physics and quantum mechanics. So please bear with me regarding any ...