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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81 views
Quantum uncertainty can explain the Riemann Hypothesis?
In the recent paper "Riemann Hypothesis as an Uncertainty Relation" (http://arxiv.org/abs/1304.2435) the author claims that the presence of zeros out of the critical line may lead to the violation of ...
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43 views
Partial Measure Probability
Let be a
$$|\psi\rangle = \dfrac{3}{5\sqrt{2}}|00 \rangle- \dfrac{3i}{5\sqrt{2}}|01 \rangle+ \dfrac{2\sqrt{2}}{5}|10 \rangle - \dfrac{2\sqrt{2} i}{5}|11 \rangle$$
state with two qubits. ...
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1answer
85 views
The Klein–Gordon equation
As we know that the Schrödinger equation presents basis of Quantum Mechanics and analogy with Newton second law in Classical Mechanics, I thought that relativistic interpretation of Schrödinger ...
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1answer
55 views
What is paramagnetic current-current correlation?
I know what paramagnetism is. But first I want to know about the paramagnetic current and then the above-mentioned correlation?
Actually, I am working on a paper on superconductivity where I have ...
3
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1answer
105 views
The issue on existence of inverse operations of $a$ and $a^{\dagger}$
I have asked a question at math.stackexchange that have a physical meaning.
My assumption: Suppose $a$ and $a^\dagger$ is Hermitian adjoint operators and $[a,a^\dagger]=1$. I want to prove that ...
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1answer
84 views
Mysterious spectra?
In my blog post Why riemannium? , I introduced the following idea. The infinite potential well in quantum mechanics, the harmonic oscillator and the Kepler (hygrogen-like) problem have energy spectra, ...
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1answer
59 views
Angular Momentum Addition Theorem
If I have, for example a particle with $s = 3/2$ and $\ell = 2$, what are the allowed values of $j$?
I'm slightly confused because I know that $j = \ell + s$, so surely there is only one allowed ...
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0answers
31 views
When is classical mechanics valid for describing motion of atoms?
In Molecular Dynamics simulations, the Newton's equation of motion is used to calculate the time evolution of system. Once, I read in an introductory text that when the thermal de Broglie wavelength ...
12
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1answer
230 views
Classical results proved using quantum mechanics
Are there any results in classical mechanics that are easier to show by deriving a corresponding result in quantum mechanics and then taking the limit as $\hbar\rightarrow0$?
(Are there classical ...
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2answers
121 views
Quantization of orbital angular momentum
Probably a very simple question, but I can't find the answer on the Internet.
I know nearly to nothing about quantum mechanics, but in statistical physics I'm confronted with the idea that the orbital ...
1
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1answer
62 views
Maximizing Multiplicity of Einstein Solid == (Temperature = $\infty$)?
If I have a system consisting of 2 Einstein solids (A and B) is it equivalent to say that maximizing the multiplicity of the ...
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0answers
68 views
Time-dependent perturbation theory [closed]
I am a student looking to understand the question given in the URL.
I understand how to complete earlier parts of this question. But the part I struggle with is figuring out which are the allowed and ...
2
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0answers
42 views
Boundary condition Hamiltonian with point tinteractions
I`m studying the Hamiltonian with point interaction centered in $y$ in three dimensions.
I know that the elements in the domain of the Hamiltonian are of the form
$$\psi=\phi+qG^z(\cdot-y)$$
where ...
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1answer
71 views
Why does a plane wave have definite momentum?
Apologies if this is a little vague. It might not have a good answer.
Given the interpretation of $|\psi(x)|^2$ as a probability distribution it's unsurprising that a wave function that is ...
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0answers
33 views
The physical implementation of quantum annealing algorithm
From that question about differences between Quantum annealing and simulated annealing, we found (in comments to answer) that physical implementation of quantum annealing exists (D-Wave quantum ...
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1answer
97 views
Potential step and its transmission / reflection
Lets say we have a potential step with regions 1 with zero potential $W_p\!=\!0$ (this is a free particle) and region 2 with potential $W_p$. Wave functions in this case are:
\begin{align}
...
5
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2answers
133 views
Bell's Theorem graph
My friends and I got into an argument about determinism, and I brought up that quantum events are random. But I couldn't prove it.
I found the Wikipedia page on Bell's theorem, which seems to imply ...
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3answers
84 views
Observer effect, do this mean literally someone or just any interaction with other matter?
I am a layman and was wondering, the quantum observer effect. The regular notion to laymen seems to be literally "if you look at it", but as I am coming to understand the world I live in better I feel ...
3
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1answer
80 views
Questions about entanglement from a laymen/quantum hobbyist
Please note I am not a physicist I just read every article I can on it, I understand a good amount on it though. But no maths. (currently trying to learn the maths)
By what means can we as humans ...
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1answer
59 views
Why uncertainity is minimum for coherent states?
While reading for quantum damped harmonic oscillator, I came across coherent states, and I asked my prof about them and he said me it is the state at which $\Delta x\Delta y$ is minimum. I didn't ...
2
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1answer
79 views
Nonseparable Hilbert space
What kind of things can go wrong if we try to do quantum mechanics on a nonseparable Hilbert space? I have heard that usual mathematical manipulations that we take for granted will no longer hold. ...
2
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2answers
101 views
Seeing colors: photons vs waves
As an atmospheric physics major I am familiar with electromagnetic radiation in the atmosphere and what dictates what wavelength objects will emit at. When observing radiation in the atmosphere it is ...
1
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1answer
154 views
I am interested in learning Quantum Computing what should I do? [closed]
I wish to learn about quantum computing which seems to be a topic of hot research and overall just intrigues me. I have a strong background in discrete mathematics and number theory. And am a pretty ...
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0answers
27 views
Partial Measurement in Computational Basis
I am reading my lecture, here say: For example, we can measure the first qubit of system described by the state $|\psi\rangle = \sqrt{\dfrac{2}{3}}|0\rangle \otimes \dfrac{|0\rangle - ...
3
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2answers
92 views
What is a symmetry of a physical system?
If I understand correctly, in many context in physics (quantum mechanics?), a physical system is specified by giving its Hamiltonian. I also hear that symmetries are rather essential.
As far as the ...
2
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2answers
94 views
Why the hydrogen radial wave function is real?
Why the hydrogen radial wave function is real?
Is it a coincidence?
2
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1answer
74 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
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1answer
57 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
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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 ...
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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 ...
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3answers
156 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 ...
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3answers
323 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
$$
H = \alpha[\sigma_z^1 + \sigma_z^2] + ...
1
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0answers
88 views
Is there a physical reason for level repulsion and avoided crossings?
Suppose we have a Hamiltonian that depends on various real parameters. When tuning the values of these parameters, the energy eigenvalues will often avoid crossing each other. Why?
Is there a ...
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1answer
66 views
Question about a finite time interval step in the derivation of the Feynman path integral in Sakurai
This may be a possible errata but Sakurai (pp 126 in the 2nd Edition) states that starting with
$$S = \int dt \,\,\scr{L_{\mathrm{classical}}}$$
Looking at a finite-time-interval of the action:
...
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0answers
74 views
Unitary Operator apply to Entangled vector
I am trying of resolve this exercise: Show that if $|\psi \rangle$ is an entangled state of two Qbits, then the application of a unitary operator of the form $U_1 \otimes U_2$ necessarily generates an ...
2
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2answers
71 views
Nature of Perturbed state in Perturbation Theory?
I'm interested in the Nature of Perturbed state in Perturbation Theory.
The first order perturbed state is given by
$$\psi^{(1)}_{n}=\Sigma_{m}a_{m}\psi^{(0)}_{m}.$$
Where
...
1
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2answers
88 views
Why does the wave description say that probability oscillates, while the phase interpretation says constant amplitude?
The wave description of a particle illustrates an oscillating probability of the particle being found in any point in space.
When a particle travels, it carries along with it a phase that oscillates ...
1
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1answer
69 views
Slater determinant space vs real space
Could someone explain to me what this snippet of text means?
Although it is possible for DMC to be used as a benchmark for
quantum-chemistry methods and vice versa, DMC does not operate in a
...
3
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4answers
183 views
Are photons deterministic?
I propose the following scenario:
At $t=0$, a photon is emitted from a star. At $t=n$, said photon is received and interpreted by some detector.
My question is whether or not it is accurate to say ...
3
votes
1answer
130 views
How does a state in quantum mechanics evolve?
I have a question about the time evolution of a state in quantum mechanics. The time-dependent Schrodinger equation is given as
$$
i\hbar\frac{d}{dt}|\psi(t)\rangle = H|\psi(t)\rangle
$$
I am ...
1
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2answers
86 views
Does performing a measurement on a system change its internal energy?
I'm studying Quantum Mechanics in my spare time from a general point of view (no technical details) so some fundamental question came into my mind:
How is it possible to detect a single photon ...
3
votes
5answers
228 views
Math of eigenvalue problem in quantum mechanics
I learned the eigenvalue problem in linear algebra before and I just find that the quantum mechanics happen to associate the Schrodinger equation with the eigenvalue problem. In linear algebra, we ...
1
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1answer
81 views
normalizing a wavefunction
I have a homework problem that I can't get started on, below is the first bit. I feel like I should just be able to integrate to find $C$ but I get a divergent integral. Can someone give me a hint as ...
2
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0answers
91 views
Black & Scholes and the Quantum Mechanics
I am interested in the link between the Black & Scholes equation and quantum mechanics.
I start from the Black & Scholes PDE
$$
\frac{\partial C}{\partial t} = -\frac{1}{2}\sigma^2 S^2 ...
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0answers
58 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):
$x_H(t)=x_H(0)cos(\omega t)+(1/m\omega)p_H(0)sin(\omega t)$
...
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0answers
43 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
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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
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0answers
31 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
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3answers
402 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) = ...
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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 ...
