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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Can a quantum mechanical system have more than one wave-function?

I was told that a quantum mechanical system is completely determined by its wave function. But superposition principle says that given two wave functions of some system, a linear combination of them ...
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2answers
93 views

Why does a electric Potential have to be real, but not a Potential in quantum mechanics?

So I had this Problem when I had to learn about classical electromagnetism: Why is it, that we use complex numbers when calculating stuff, but in the end only the real part is important (for example ...
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36 views

“Instantaneous” time stepping with time dependent Hamiltonian Schrodinger equation

The Schrodinger equation for time-dependent Hamiltonian is $$i\hbar\frac{d}{dt}\psi(t) = H(t)\psi(t) \, .$$ I know that the "instantaneous" solution of this equation is $$\psi(t+dt) = e^{-\frac{i}{...
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45 views

Why Does there Have to be Linearity in Ket and Skew Symmetry?

I'm reading Shankar's "Principles of Quantum Mechanics," and on page 8 he states that one axiom in Dirac notation is linearity in ket, and because they are also skew symmetric there is anti-linearity ...
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28 views

Book Recommendation: Quantum optics

Could you suggest me a list of books for understanding Quantum Optics for students who have studied Introductory Q.M.(such as Griffiths). It would be grateful if you distinguish between readable one(...
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3answers
112 views

What is the cause of quantum entanglement? [duplicate]

I understand the idea of quantum entanglement - where what happens to one particle in one location instantly effects another particle in another location, even if separated by millions of miles. But ...
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0answers
28 views

Planck's temperature - why is there a maximum? [duplicate]

Why do the laws of physics break after Planck's temperature?
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0answers
26 views

Ratio of de Broglie wave length [closed]

Electron A has twice the kinetic energy as electron B. What is the ratio of de Broglie wavelengths of electron A and B? - this was a question given to me in advanced higher physics but I got a bit ...
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1answer
34 views

Relationship Between Magnetic Dipole Moment and Spin Angular Momentum

I am reading Introduction to Quantum Mechanics 1st edition by David J. Griffiths and I have a couple questions about this section on page 160. A spinning charged particle constitutes a magnetic ...
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32 views

Identical bosons with spin interactions eigenstates

Suppose that we have two particles where each of them has s=1 and it is in a harmonic oscillator potential and there is also a spin interaction. The hamiltonian of the system is :$$H=\frac{p_1^2}{2m}+\...
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0answers
30 views

Distribution of quantum beating among spectral frequencies

Let's imagine that we have 3-level system: ground state $\vert 0 \rangle$ and two excited states $\vert 1 \rangle$, $\vert 2 \rangle$ with similar energies $\hbar \omega _1$ and $\hbar \omega _2$ ...
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+50

Significance of the exception to Gleason's Theorem when n = 2

Gleason's Theorem famously asserts that (appropriately defined) measures on the lattice of a complex Hilbert space can be implemented by density operators via the trace operation, except in the case ...
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0answers
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Rigorous way of box normalisation

This is follow up from an answer to my previous question about unitarity in rigged Hilbert space. As it turns out, that there is no idea of unitarity in rigged Hilbert space (hence no meaningful QM ...
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2answers
91 views

How to visualize an electron existing in two different places at the same time?

Let's consider a hypothetical situation where there are two electrons. The first electron is in superposition, simultaneously existing in two different locations. Let the locations be ...
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3answers
134 views

Can a physical wavefunction be non-smooth (its first derivative is discontinuous)?

Here's an argument that might support the statement that such a non-smooth wavefunction is not physical: You cannot add a finite number of smooth functions to get a non-smooth function. By fourier ...
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1answer
35 views

What is the angular velocity of the electron?

An electron has angular momentum. Shouldn't it also have angular velocity? Ignoring the g-factor (just for the order of magnitude approximation) and the fact that an electron is not a sphere the ...
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1answer
58 views

Norm preserving Unitary operators in Rigged Hilbert space

If we take the free particle Hamiltonian, the eigenvectors (or eigenfunctions), say in position representation, are like $e^{ikx}$. Now these eigenfunctions are non-normalisable,so they don't belong ...
2
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1answer
145 views

Strange implication of the relativistic invariance of the Dirac equation

At least as normally formulated, the law of transformation of a wave function solution of the Dirac equation to another inertial frame seems to indicate that if observer 1 is certain the particle is ...
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1answer
67 views

Understanding Quantum Harmonic Oscillator derivation

I'm using this pdf as a reference. Basically, I want to solve equation 0.3, which can be simplified to equation 0.5. The solution is in the form $$ \Psi(u)=h(u)e^{\frac{-u^2}{2}}$$ where $h(u)$ can ...
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0answers
40 views

Density of States for a separable hamiltonian

There are $N$ non interacting electrons in a potential well: \begin{align} H&= -{1 \over 2 } \nabla^2 + U(x,y,z) \\ U(x,y,z)&={1\over2}\omega^2z^2 \; \mbox{for} \; (x,y) \in [0,L]\times [0,L]; ...
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0answers
69 views

Free Particle: Time dependence of expectation value of position Paradox

It would be really appreciated if somebody could clarify something for me: I know that stationary states are states of definite energy. But are all states of definite energy also stationary state? ...
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1answer
71 views

An example of a nonlinear but deterministic physical transformation in Hilbert space

Supposedly all physically realisable transformations are either linear or non-deterministic (measurements are not linear transformations, but they are non-deterministic, from the perspective of the ...
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0answers
27 views

Normalize plane wave on an infinite domain.

I need to make an exercise related to quantum mechanics. (Specifically I need to apply Fermi's golden rule where the initial and final states are both plane waves). The system is 1 dimensional, ...
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0answers
41 views

At most $N$ gapless charge/spin modes in a system of $N$ coupled 1D chains?

Leon Balents and Matthew P. A. Fisher claimed the following without any further explanation ($N$ is the number of chains) For a system of $N$ coupled 1D chains, the number of gapless charge modes ...
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37 views

Current Conservation [on hold]

Why is current conservation important? Specifically, in QFT and String Theory lecture notes and textbooks it's always stated that current conservation is important because it helps maintain quantum ...
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7answers
1k views

Why is a Hermitian operator a “quantum random variable”?

To me, as a stupid mathematician, a random variable is a measurable function from some probability space $(\Omega, \sigma, \mu)$ to $(\Bbb{R}, B(\Bbb{R}))$. This makes sense. You have outcomes, events,...
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1answer
45 views

Angular momentum in annihilation $n\overline{n} \rightarrow \pi^0 \pi^0$

Consider the annihilation of a neutron by an anti-neutron $$ n\overline{n} \rightarrow \pi^0 \pi^0 $$ so that the initial relative angular momentum is zero. Because the spin of neutrons is $1/2$, $J_i$...
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0answers
37 views

How can $\hat p = - i \hbar \partial_q$ be derived starting from the definitions of $\hat q$ and $\hat p$ in terms of creation/destruction operators? [duplicate]

Consider the position and momentum operators $\hat q$ and $\hat p$, defined respectively in terms of creation and destruction operators in the usual way: $$ \hat q = c (\hat a + \hat a^\dagger), \...
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0answers
39 views

Energy Conservation in Changing Potential Well

If you prepare a particle in a basis state, $|n\rangle$ of an infinite potential well of length $L$, the energy of that state will be $\langle E\rangle = E_n$, with zero variance. If you then ...
1
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1answer
138 views

How to find this spin wavefunction? [closed]

If an electron is in a state that the probability of measuring spin along the +x axis is $P(+x)=\dfrac{1}{2}$ and the probability of measuring spin along the +y axis is $P(+y)=\dfrac{1}{2}$, what is ...
3
votes
1answer
85 views

Is there any Hamiltonian that contains time derivative? [duplicate]

Quantum mechanics is governed by Schrodinger's equation: $$\hat{H}\psi=i\hbar\partial_t \psi$$ It seems that Hamiltonian acts on wave functions like a time derivative. Just out of curiosity, is ...
3
votes
1answer
117 views

Replacing fermionic operators with their Fourier transform and boundary conditions

In the section 4.1 of Quantum Computation by Adiabatic Evolution, Farhi et al proposes a quantum adiabatic algorithm to solve the $2$-SAT problem on a ring. To compute the complexity of the algorithm ...
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4answers
779 views

If an isolated quantum system consists of only one particle, is it possible for it to be in a mixed state?

Mixed states are defined as the statistical ensemble of pure states. Classically, I understand the word, "statistical" referring to a system with a large number of microscopic particles. So if I go ...
3
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2answers
77 views

Meaning of non-degenerate photon pair

I am seeing in a lot of papers about quantum optics the term "non-degenerate photon pair", which seems like a very important concept. This may seem like a silly question, but I am an EE undergrad who ...
2
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0answers
84 views

Some questions about the Kitaev Chain Model

In the paper,'Unpaired Majorana Fermions in Quantum Wires', Kitaev shows that unpaired Majorana Modes can be found at the end of a Quantum Wire for certain conditions. The effective Hamiltonian ...
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0answers
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Is there an explanation to Heisenberg's Uncertainty principle? [duplicate]

I watched a video witnessing Heisenberg's Uncertainty principle in action. I'm wondering is there an "explanation" (not on basis of observations) to it? p.s. Consider me a noob before answering.
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2answers
102 views

Total spin of system of two spin-$1/2$ particles

Consider a quantum system of two spin one half particles. Let $\alpha(1)$ be 'spin up' for first system, and $\beta(1)$ 'spin down' for first system, and likewise for second system. We have $$ \chi = \...
3
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1answer
53 views

Is it possible to create a pair of polarized, polarization-entangled photons?

Is there a light source which emits (mostly) polarization-entangled pairs of photons that have a known polarization angle, e.g. a certain angle in relation to the orientation of the source? Applying ...
3
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1answer
60 views

Tensor product representation of $SO(3)$ in the Hilbert space of particle with spin $S$

For a particle with a spin $S$, the rotation operator is given by $$ e^{iJ_i\theta/\hbar} $$ where $J_i$ is the component of the total angular momentum along the direction of the rotation axis. The ...
3
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2answers
91 views

What kets represent on QFT?

In Quantum Mechanics kets are used to represent states of a system. This is indeed well written in the first postulate of Quantum Mechanics which states that to describe a quantum system we use a ...
3
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1answer
42 views

Aim of photon gun in a double-slit experiment

Hope someone can enlighten me on the following questions: In a double-slit experiment with photon, how is the photon gun aimed? If the photon gun is set up to aim at the barrier space between the ...