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-...

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Interactions preserving separability

Consider the interaction (described by a unitary matrix U) of two qubits initially in a separable state |ab⟩ = |a⟩ ⊗ |b⟩, such that after interaction the composite system is in state U|ab⟩. Are there ...
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1answer
45 views

Can quantum computer provide random or just pseudo-random number, or none of both? [closed]

Can quantum computer provide random or just pseudo-random number, or none of both? It's a bit confusing me, since collapse of wave function once measured.
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1answer
68 views

What is the difference between Quantum Gravity, Loop Quantum Gravity, Quantum Geometrodynamics, and Relativistic Quantum Mechanics? [closed]

What is the difference between Quantum Gravity, Loop Quantum Gravity, Quantum Geometrodynamics, and Relativistic Quantum Mechanics? As far as I know, they are all theories made to unify QM and GR. But ...
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1answer
54 views

Plotting hydrogen wave functions

This may sound a bit dumb but how do I plot the hydrogen wave functions? For example, what is exactly being represented [in this image][1]? Is it just the norm-squared of the wave function and is the ...
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2answers
85 views

Heisenberg uncertainty principle

In the double slit experiment, an electron interferes with itself and creates the pattern because it is in a superposition, traveling through both slits. If we place a detector at one slit, the wave ...
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1answer
46 views

Most probable radius of hydrogen in its ground state [closed]

I'm having trouble understanding how we do this. I know we must find the probability density function and then we can optimise it to find the most probable radius. I thought we would just take the ...
42
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9answers
6k views

Extension of Schrödinger's cat thought experiment

My question is quite simple. In the thought experiment of Schroedinger's cat: When the scientist measures the state of the cat, its wavefunction collapses into either the alive or dead state. But ...
4
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1answer
95 views

Energy Spectrum of Star Products

We have that a property of the transition operator defining c-equivalence (or star equivalence from equation 1 in Bertelson) is \begin{align*} T(f\star_Mg)=T(f)\star'T(g)\,, \end{align*} where $\...
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1answer
47 views

Examples of Matrix Product State(s)

Matrix product states(MPS) is a way of representing a (many-body) wavefunction. The method has been described in, https://arxiv.org/abs/1008.3477 However, would it be possible to see a concrete ...
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1answer
66 views

How to find the corresponding Hamiltonian in quantum, if Hamiltonian in classical mechanics is given? [closed]

Hamiltonian in classical mechanics is $$H=wxp $$ $x=$ position, $p=$ momentum coordinate. Find the corresponding Hamiltonian in quantum mechanics!
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28 views

Doubt regarding scattering and bound states in quantum mechanics

I just started studying quantum mechanics from Introduction to Quantum Mechanics by D. J. Griffiths. At the beginning of the second chapter, he proves that we cannot have negative energies in the time-...
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2answers
61 views

Half-integer angular momentum

Does half-integer angular momenta mean that the particle will always be found spinning? For example, if a particle is in a $l=\frac{1}{2}$ state, this means $ m=\pm\frac{1}{2}$ and since $L_z=\hbar m ...
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49 views

Gravitational analogue to the hydrogen atom

I'm not sure what to make of this problem from Griffiths' Intro to QM: Suppose the earth made a transition to the next lower level $(n-1)$. How much energy (in joules) would be released? What ...
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3answers
149 views

When we say electron spin is 1/2, what exactly does it mean, 1/2 of what?

When we say electron has spin of $\frac{1}{2}$, is that the value of the total spin of electron, or the projection on z axis, or the spin quantum number? When we say "electron has spin of $\frac{1}{2}...
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1answer
35 views

What does it mean to have a transmission coefficient 1.03*10^-3

I solved a potential barrier problem. E=4.5ev V0=5eV barrier width a=950pm The transmission coefficient came out to be 1.03*10^-3 I was wondering what this means? isn't the transmission probability ...
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1answer
32 views

Is 3D optical lattice just a stack of 2D lattices?

I am confused about the idea of 3D optical lattice. Many papers use 3D optical lattice to study bosons behavior, but is it really a 3D system where atoms interact in all three directions or is it just ...
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0answers
17 views

Darwin term affecting hydrogen s-states

The Darwin term, a correction to the non-relativistic hydrogen Hamiltonian due to the zitterbewegung of the electron, is given by $$H_{Darwin}=\frac{e^2\hbar^2}{8m^2c^2\epsilon_{0}}\delta^3(\...
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3answers
51 views

Measuring different components of spin simultaneously

I'm reading Griffiths Introduction to QM and I'm having trouble understanding why you can't simultaneously measure the x,y and z components of spin. I know that the uncertainty principle prevents this ...
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36 views

Are there exact analytical solutions to the electronic states of the hydrogen molecular ion $\mathrm H_2^+$?

The hydrogen molecular ion (a.k.a. dihydrogen cation) $\mathrm H_2^+$ is the simplest possible molecular system, and as such you'd hope to be able to make some leeway in solving it, but it turns out ...
5
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1answer
128 views

How did Heisenberg come up with matrix mechanics?

I have learnt that matrix mechanics came before Schroedinger's wave mechanics, however introductory quantum mechanics textbooks introduce you to wave mechanics first. The way in which the transition ...
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1answer
129 views

Classical Mechanics as an approximation of Quantum mechanics [closed]

I want to show an equality: We know from Ehrenfest's theorem that $$ \frac{d \langle x \rangle(t)}{dt}= \left\langle \frac{\partial H}{\partial p} \right\rangle $$ I'd like to derive the ...
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2answers
293 views

Atomic Weight and Time Dilation

So, this might sound kind of ridiculous but I was thinking about Relativity and since Gravity is a warping of Space-Time, or Time Dilation, why don't we measure Atomic Mass in Units of Time Dilation? ...
5
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2answers
105 views

Why doesn't this experiment violate the Uncertainity Principle?

Is it possible to slow an electron in such a way(for example using a cyclotron to decelerate the electron ) that it completely stops. And since we created the slowing mechanism we might be able to ...
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1answer
99 views

How is hydrogen fine structure currently accounted for? [closed]

At a usually reliable site, Hyperphysics, the fine structure of Hydrogen is accounted for by the interaction between the B-field generated by the orbit of the electron, $0.4\:\mathrm{T}$ at $1s$ and $...
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0answers
39 views

Can a quark be changed to a different flavour?

For example, is it possible to change an up quark into a down quark or vice versa? If so, what is the practical process for doing such a thing? What is the theory behind it? For an example, lets say ...
3
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0answers
44 views

Energy term in Wavefunction Normalization

I recently started learning quantum mechanics and when I solved the Schrödinger equation for the Hydrogen atom, in particular the Radial equation, I found that I had normalized it but a term in the ...
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32 views

Must entangled particles be connected by some means to stay entangles

The people on this site are far more knowledgeable than I am and I probably don't belong here but my questions always seem to get answered to my satisfaction and I end up learning something. I have ...
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1answer
42 views

counting normal modes

I'm not sure if my confusion is substantive or merely semantic. So here's the most naïve way to frame it: A free $N$-atom molecule has $3N-6$ vibrational normal modes, with each mode having fixed ...
4
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1answer
52 views

When and why are effective Hamiltonians used?

I'm wondering, are there general physical principles behind writing down quantum evolutions in terms of effective Hamiltonians? I'd love a kind of big-picture explaination of their use. For example, ...
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1answer
78 views

Where do people go (online) to present big ideas they have discovered? [closed]

I can't realistically travel, but is there somewhere online where I can present some ideas? Or do I just put it on arXiv and hope someone important reads it?
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1answer
166 views

When particle number can change in quantum physics?

Let me write a paragraph from D.Tong lecture notes on QFT-chapter2 when he is talking about non-relativistic limit of scalar quantum field theory : A related fact is that the conserved charge $Q=\...
2
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0answers
46 views

How does the Pauli-exclusion principle work if space is infinitely divisible?

How does the Pauli-exclusion principle work if space is infinitely divisible? Naively any two fermions should always be in different quantum states unless they are separated by an infinitesimally ...
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11 views

Energy independent tunneling rate

I was wondering if there are any examples of potential barriers for which the tunneling probability is independent of particle energy (ignoring any infinities of course). It seems that from the WKB ...
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1answer
49 views

Infinite square well - periodic boundaries

If we have an infinite square well, I can follow the usual solution in Griffiths but I now want to impose periodic boundary conditions. I have $\psi(x) = A\sin(kx) + B\cos(kx)$ with boundary ...
2
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1answer
37 views

Is the variational method valid when discrete spectrum eigenfunctions are in finite number?

In the proof of the variational method to estimate the ground state energy of a system, that is $$ \newcommand{\ket}[1]{\lvert{#1}\rangle} \newcommand{\bra}[1]{\langle{#1}\rvert} \newcommand{\braket}[...
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0answers
20 views

Eigen energy of the Landau levels in a tilted magnetic field

The problem pertains to a fermi gas in a tilted magnetic field confined by a harmonic potential in the z direction. I chose the vector potential $(0,ax-bz,0)$. I obtain the following hamiltonain with ...
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0answers
31 views

Invariance of State Vector under Two Operations

I am trying to understand why if you measure one non degenerate operator you get a new state w1v let's say with w1 eigenvalue, then let's say u measure a new operator that has degenerate eigenvalue v ...
3
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1answer
58 views

Is there an angular velocity operator in quantum mechanics?

In classical mechanics we can write as velocity of a rotating object $\vec{v} = \vec{\omega} \times \vec{r} $ or in analogy the momentum $\vec{p} = m (\vec{\omega} \times \vec{r})$ using the angular ...
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2answers
44 views

How does the uncertainty product $\Delta x \Delta p$ behave for the bound states of the triangular potential?

As has been remarked earlier, if you take an unbounded potential $V(x)$ (so that all the eigenstates are bound) and you look at the uncertainty product $\Delta x\Delta p$ as a function of the index $n$...
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2answers
80 views

De Broglie- Bohm Quantum Theory

From what I have read the Standard Model of Particle Physics uses quantum mechanics,special relativity, along with other assorted mathematics to make predictions and provide a framework for QED, QCD, ...
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0answers
75 views

Why don't we have to go through the Lagrangian in QM? [duplicate]

In classical mechanics, I remember whenever we calculated the Hamiltonian, we'd first have to calculate the Lagrangian, and then we'd get the Hamiltonian through the definition: $$H= \sum\dot q_ip_i-...
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votes
1answer
40 views

Quantum vacuum thruster and conservation of momentum [duplicate]

I have been reading about the quantum vacuum thruster on Wikipedia and I think I understand the idea of virtual particles being created and destroyed but what I don't understand is how this is ...
0
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0answers
30 views

How to apply the time evolution operator on a 2 level system

I'm struggling to understand how to actually solve analytically the time evolution of a given initial state with the Hamiltonian \begin{equation} H =\epsilon*\sigma_z + \Delta*\sigma_x, \end{equation} ...
1
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1answer
37 views

Why can precomputed sets of lattice QFT field configurations be used to measure arbitrary observables?

My knowledge of quantum mechanics is rusty and my understanding of (lattice) quantum field theory on a very novice level at best, so it is likely my whole question is based on completely wrong ...
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0answers
23 views

about the motion of electrons inside the atom [duplicate]

My question is very basic question.I am somehow not able to understand it. bohr's theory says that the electron can only revolve in orbits which they have quantised angular momentum so they must ...
12
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2answers
984 views

How should Dirac notation be understood?

If vectors $|\vec{r}⟩$ and $|\vec{p}⟩$ are defined as $$ \hat{\vec{r}} |\vec{r}⟩ = \vec{r} |\vec{r}⟩ \\ \hat{\vec{p}} |\vec{p}⟩ = \vec{p} |\vec{p}⟩ $$ then one can see that products like $$ ⟨\vec{...
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0answers
20 views

Function of operator quantum mechanics [duplicate]

Help me to prove this $$e^Ae^B=e^{A+B}e^{\frac{1}{2}[A,B]}$$ $A$ not commute with $B$, but $A and $B commute with $[A,B]$.
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Specific microstate(s) corresponding to total angular momentum quantum number

Given a certain number of electrons in a certain electronic configuration (say, d$^2$ or (n$_1$p)(n$_2$d)), all combinations of the quantum numbers $m_l$ and $m_s$ can be constructed. Each of these ...
4
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1answer
89 views

Understanding the relationship between Phase Space Distributions (Wigner vs Glauber-Sudarshan P vs Husimi Q)

I am moving into a new field and after thorough literature research need help appreciating what is out there. In the continuos variable formulation of optical state space. (Quantum mechanical/Optical)...
3
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1answer
61 views

Quantum master equation and off diagonal terms

I have a couple of related questions What is exactly the difference between the quantum master equation and the regular master equation? My understanding is that the normal master equation is used ...