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
72 views
Understanding de Broglie Wavelengths
I understand the derivation and calculation of de Broglie wavelengths, but what exactly does the wave of a particle represent? What does the wavelength of a particle mean? I'm assuming it's not the ...
2
votes
1answer
56 views
Why is the total interaction cross section larger for incident particles with lower energy?
The cross section of a nuclear interaction is a measurement of the probability of that interaction occuring. These probabilities are typically presented in terms of barns ($10^{-28}$ m$^2$) as a ...
3
votes
1answer
92 views
Measurement and probability for quantum states
Suppose that the physical system is in generic state $|\psi\rangle$. Show that $\sum_{\lambda}p^2_{\lambda} = 1$ to an observable $O$, if and only if $\Delta O = 0$. ($\Delta O$ is a standard ...
0
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1answer
57 views
Why do people say the phase oscillates in time and the amplitude stays the same but the intensity of a traveling beam does oscillate with time?
I'm confused why people say the phase oscillates in time and the amplitude stays the same (the reason for having complex numbers). But on the other hand, the intensity of a traveling beam does ...
5
votes
3answers
153 views
How to express a Hamiltonian operator as a matrix
Suppose we have Hamiltonian on $\mathbb{C}^2$
$$H=\hbar(W+\sqrt2(A^{\dagger}+A))$$
We also know $AA^{\dagger}=A^{\dagger}A-1$ and $A^2=0$, letting $W=A^{\dagger}A$
How can we express $H$ as $H=\hbar ...
10
votes
3answers
317 views
How to tackle 'dot' product for spin matrices
I read a textbook today on quantum mechanics regarding the Pauli spin matrices for two particles, it gives the Hamiltonian as
$$
H = \alpha[\sigma_z^1 + \sigma_z^2] + ...
1
vote
0answers
86 views
Is there a physical reason for level repulsion and avoided crossings?
Suppose we have a Hamiltonian that depends on various real parameters. When tuning the values of these parameters, the energy eigenvalues will often avoid crossing each other. Why?
Is there a ...
0
votes
1answer
65 views
Question about a finite time interval step in the derivation of the Feynman path integral in Sakurai
This may be a possible errata but Sakurai (pp 126 in the 2nd Edition) states that starting with
$$S = \int dt \,\,\scr{L_{\mathrm{classical}}}$$
Looking at a finite-time-interval of the action:
...
1
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0answers
72 views
Unitary Operator apply to Entangled vector
I am trying of resolve this exercise: Show that if $|\psi \rangle$ is an entangled state of two Qbits, then the application of a unitary operator of the form $U_1 \otimes U_2$ necessarily generates an ...
2
votes
2answers
71 views
Nature of Perturbed state in Perturbation Theory?
I'm interested in the Nature of Perturbed state in Perturbation Theory.
The first order perturbed state is given by
$$\psi^{(1)}_{n}=\Sigma_{m}a_{m}\psi^{(0)}_{m}.$$
Where
...
1
vote
2answers
85 views
Why does the wave description say that probability oscillates, while the phase interpretation says constant amplitude?
The wave description of a particle illustrates an oscillating probability of the particle being found in any point in space.
When a particle travels, it carries along with it a phase that oscillates ...
1
vote
1answer
69 views
Slater determinant space vs real space
Could someone explain to me what this snippet of text means?
Although it is possible for DMC to be used as a benchmark for
quantum-chemistry methods and vice versa, DMC does not operate in a
...
2
votes
4answers
180 views
Are photons deterministic?
I propose the following scenario:
At $t=0$, a photon is emitted from a star. At $t=n$, said photon is received and interpreted by some detector.
My question is whether or not it is accurate to say ...
3
votes
1answer
128 views
How does a state in quantum mechanics evolve?
I have a question about the time evolution of a state in quantum mechanics. The time-dependent Schrodinger equation is given as
$$
i\hbar\frac{d}{dt}|\psi(t)\rangle = H|\psi(t)\rangle
$$
I am ...
1
vote
2answers
85 views
Does performing a measurement on a system change its internal energy?
I'm studying Quantum Mechanics in my spare time from a general point of view (no technical details) so some fundamental question came into my mind:
How is it possible to detect a single photon ...
3
votes
5answers
223 views
Math of eigenvalue problem in quantum mechanics
I learned the eigenvalue problem in linear algebra before and I just find that the quantum mechanics happen to associate the Schrodinger equation with the eigenvalue problem. In linear algebra, we ...
1
vote
1answer
78 views
normalizing a wavefunction
I have a homework problem that I can't get started on, below is the first bit. I feel like I should just be able to integrate to find $C$ but I get a divergent integral. Can someone give me a hint as ...
2
votes
0answers
88 views
Black & Scholes and the Quantum Mechanics
I am interested in the link between the Black & Scholes equation and quantum mechanics.
I start from the Black & Scholes PDE
$$
\frac{\partial C}{\partial t} = -\frac{1}{2}\sigma^2 S^2 ...
0
votes
0answers
57 views
Quantum harmonic oscillator. Finding operators
Problem:
I'm trying to verify that $p_H(T)$ and $x_H(T)$ satisfy the following equations, (by solving the Heisenberg equation):
$x_H(t)=x_H(0)cos(\omega t)+(1/m\omega)p_H(0)sin(\omega t)$
...
0
votes
0answers
40 views
Wave equations for two intervals at Potential step
Lets say we have a potential step as in the picture:
In the region I there is a free particle with a wavefunction $\psi_I$ while in the region II the wave function will be $\psi_{II}$.
Let me ...
1
vote
1answer
60 views
Can we use intensities in the superposition principle?
In using the superposition principle to calculate intensities in interference patterns, can we add the intensities of the waves instead of their amplitudes? I think that amplitude account for the ...
1
vote
0answers
30 views
Trotter splitting and entanglement entropy
I have heard that a numerical solution to the Schrodinger equation using the Trotter splitting formula for a many-body Hamiltonian can cause an artificial increase in the entanglement entropy. I was ...
13
votes
3answers
399 views
Quantum mechanics - how can the energy be complex?
In section 134 of Vol. 3 (Quantum Mechanics), Landau and Lifshitz make the energy complex in order to describe a particle that can decay:
$E = E_0 - \frac{1}{2}i \Gamma$
The propagator $U(t) = ...
0
votes
0answers
33 views
Is it easier to determine the number of states with raising/lowering operators or using scattering?
A particle is bound by
$$V(x) = \begin{cases}\infty,& x <0 \\ \frac{-32\hbar^2}{ma}, & x\le a \\ 0, & x \le a\end{cases}$$
a) how many states are there?
i'm attempting ...
0
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0answers
35 views
Do the other properties of a particle also have a phase?
Particles have a phase that oscillates in space-time. We know this because particles have a phase frequency (De Broglie wavelength) and this is why they interfere in space, like in the double slit ...
3
votes
0answers
99 views
Quantum Electrodynamics
I was wondering if anyone could give a simple explanation of how light interacts with matter. From what I have read in QED, electrons will repel each other because of their ability to emit and ...
4
votes
0answers
117 views
Question about the HVZ theorem
In this paper1 the authors cite the HVZ theorem2 saying that it follows from the method used by M. Reed & B. Simon without modifications; I don't really understand this point.
Is there anyone who ...
6
votes
2answers
144 views
Why does the quantum Heisenberg model become the classical one when $S\to\infty$?
The Hamiltonian of the spin $S$ quantum Heisenberg model is
$$H = J\sum_{<i,j>}\mathbf{S}_{i}\cdot\mathbf{S}_{j}$$
I have read that when the spin quantum number $S\to\infty$, quantum fluctuation ...
5
votes
2answers
157 views
A question on the existence of Dirac points in graphene?
As we know, there are two distinct Dirac points for the free electrons in graphene. Which means that the energy spectrum of the 2$\times$2 Hermitian matrix $H(k_x,k_y)$ has two degenerate points $K$ ...
3
votes
1answer
110 views
Bloch sphere representation
Suppose you know that a qubit is either is in state $|+\rangle$ with probability $p$ or in state $|-\rangle$ with probability $1-p$. If this is the best you know about the qubit's state, where in the ...
0
votes
1answer
92 views
Energies and numbers of bound states in finite potential well
Hello I understand how to approach finite potential well (I learned a lot in my other topic here). However i am disturbed by equation which describes number of states $N$ for a finite potential well (
...
0
votes
2answers
80 views
EPR vs. EPRBB? Why can't we perform the original EPR experiment?
The EPR gedanken experiment was invented by Einstein Podolsky and Rosen in 1935.
It involved positions and momenta. In 1957, Bohm revised this gedanken experiment into one involving spins, or ...
0
votes
2answers
75 views
If inherent randomness exist in quantum mechanics, what then of eternalism implied by relativity?
I am nothing but a curious layman so don't go too technical on me.
First of all, I am well aware that a lot of people consider the question of determinism vs indeterminism to be unsolved and others ...
0
votes
1answer
66 views
Why is the energy spectrum of bound QM plane wave continuous?
Please explain it in the context of this task: we have a potential barrier that looks like $\prod$, with $E<U$. There are 3 regions:
1) no field
2) barrier
3) no field
Solution could be ...
3
votes
2answers
90 views
What is wrong with these ways of determining the mean occupation number?
Could anyone point out what went wrong in this argument?
Setup:
We have a system with 2 energy levels say with energies $0,e$ respectively.
We consider the grand canonical ensemble for the system ...
1
vote
0answers
60 views
linear response for a simple harmonic oscillator
Really sorry for this simple question, but I think it will be useful/interesting in general.
Consider a quantum simple harmonic oscillator.
Add a perturbation $H_I = -\lambda \hat{x}$
Calculate ...
2
votes
1answer
58 views
Does the observer or the camera collapse the wave function in the double slit experiment?
Ok so if we setup a camera before the slit we will find a single photon and will follow through accordingly, likewise by having a camera setup after the slit, we can retroactivly collapse the wave ...
0
votes
2answers
73 views
About Heisenberg uncertainty principle [duplicate]
What would happen if someone invented a way to measure both position and momentum precisely? If it is impossible why?
4
votes
2answers
192 views
What prevents bosons from occupying the same location?
The Pauli exclusion principle states that no two fermions can share identical quantum states. Bosons, one the other hand, face no such prohibition. This allows multiple bosons to essentially occupy ...
1
vote
0answers
26 views
Is there anything to prevent paired-up neutrons from a complete overlap
The reason "neutrons don't overlap", as DarenW explained it, has to do with intricate forces at play that take into account the spins, iso-spins and symmetry of the wavefunctions.
However, assume I ...
3
votes
4answers
239 views
Is this statement about quantum mechanics valid?
In Philosophy of Language by William G. Lycan, there are the lines:
Even apparent truths of logic, such as truths of the form "Either P or not P", might be abandoned in light of suitably weird ...
1
vote
1answer
61 views
Is a blackbody real or imagined?
In my reading of blackbody radiation I am always asked to imagine this or that body being a perfect absorber or emitter of radiation, and I am always left with the impression that a blackbody exists ...
2
votes
1answer
217 views
Bohr-van Leeuwen theorem and quantum mechanics
Preamble:
If one considers an ideal gas of non interacting charged particles of charge $q$ in a uniform magnetic field $\mathbf{B} = \mathbf{\nabla} \wedge \mathbf{A}$, then the classical partition ...
2
votes
1answer
170 views
Show that for QM operator A: $\int_{-\infty}^{\infty}\psi A^{\dagger}A\psi dx = \int_{-\infty}^{\infty}(A\psi)^*(A\psi)dx $
I need to show for $$A = \frac{d}{dx} + \tanh x, \qquad A^{\dagger} = - \frac{d}{dx} + \tanh x,$$ that
$$\int_{-\infty}^{\infty}\psi^* A^{\dagger}A\psi dx = ...
2
votes
3answers
71 views
Curious relation between the dependance in ℏ of Planck units and units dimensions
Looking at Planck units, there seems to be a curious rule between the dependance in $\hbar$ of a Planck unit and the unit dimensions of the corresponding physical quantity.
Let the dimensions of the ...
6
votes
4answers
252 views
Interference and which-path information
My understanding is that in a double-slit experiment, quantum interference disappears if which-path information is available. How is available defined? Consider the following experiment:
SPDC is used ...
0
votes
1answer
52 views
First order coherence through double slit
The state $$|\Psi \rangle = |0\rangle + \sum_j \int d\omega f_j(\omega)\hat{a}^\dagger_j (\omega) |0\rangle $$ is coming from a far field and incident on a double slit setup. Here j is the index of ...
2
votes
1answer
123 views
Coordinate representation of quantum ladder operator?
I can't seem to figure out how to derive the coordinate representation of the $a_+$ ladder operator in quantum mechanics.
I know that $a_-$ is $\sqrt{\frac{1}{2mwh}} (mwx + i\dot{p}) $ in which where ...
2
votes
2answers
276 views
Plotting $\psi$ for finite square well potential
Lets say we have a finite square potential well like below:
This well has a $\psi$ which we can combine with $\psi_I$, $\psi_{II}$ and $\psi_{III}$. I have been playing around and got expressions ...
1
vote
1answer
105 views
Finite potential well - transcendent equation for even solutions
I have a finite square well like the one on the picture below:
I have done some calculations on it and got a transcendental equation for even solutions which is like this:
$$
...
