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 ...

learn more… | top users | synonyms (4)

0
votes
1answer
40 views

Global and relative phases of kets in QM

In one of the questions I'm trying to solve it is asked to, first, compute probabilities for the respective results of the Stern-Gerlach measurements performed on each state $\lvert\psi_1\rangle$, ...
4
votes
1answer
82 views

Dirac Equation in RQM (as opposed to QFT) is written in which representation?

In introductory Quantum Mechanics treatments it is common to see the Schrödinger's equation being written, simply as: ...
-6
votes
0answers
84 views

“Wonderful weirdness” - I want to know whether I am a human being or something else [on hold]

EDIT: after moderators' comment below, I am adding this paragraph: This post is a partial satire. My question was how is this possible that, an object as big as ~50 micron is vibrating and not ...
0
votes
2answers
58 views

Why does electron respond almost instantaneously on nucleus' displacement due to the difference in mass of it and the nucleus?

In Born Oppenheimer Approximation, we take note of the great difference between the mass of the electrons and nuclei. But, I have not been able to understand this statement quoted from Molecular ...
-4
votes
1answer
49 views

Why do some stars become end up as black holes? [on hold]

The answer involves the gravity and the internal pressure within the star. These two things oppose each other -- the gravitational force of the star acting on a chunk of matter at the star's surface ...
1
vote
0answers
31 views

Probability of measuring a pure qubit state after some unitary rotation [on hold]

Suppose I have the prepared state $$|+\rangle = \frac{|0\rangle + |1\rangle}{\sqrt{2}}$$ and the unitary $Z_{\pi/2}$ which rotates a state in the Bloch sphere by $+\pi/2$ about the $z$-axis. As I ...
3
votes
5answers
181 views

Where does $\hat{P}\psi(x) = -i\hbar \partial_x \psi(x)$ come from?

It's a very basic question, where does the relation $$\hat{P}\psi(x) = -i\hbar \partial_x \psi(x)$$ for any square integrable $\psi(x)$ come into existence? Some texts I found states that the above ...
3
votes
1answer
32 views

What are “interferences of higher order” in the context of Born rule and triple-slit diffraction?

This question relates to the paper commented in this 2010 article. The paper itself is Ruling Out Multi-Order Interference in Quantum Mechanics; it is the discussion of a triple-slit interference ...
-1
votes
2answers
106 views

Do conservation laws contradict quantum mechanics? [on hold]

Take for example the double-slit experiment interpreted in the Copenhagen sense. The particle leaves as an object with mass, yet passes through the slits as a massless wave, only to collapse again as ...
5
votes
1answer
92 views

Von Neumann entropy of mixtures of coherent states

I'm trying to calculate the Von Neumann entropy of statistical mixtures of coherent states. The problem is that such states are in general non-Gaussian, so one cannot follow the formalism developed ...
0
votes
0answers
39 views

Quantum tunneling and the Gamow Factor

I've seen the equation for the probability of particles overcoming the Coulomb Barrier in the following form: $$P(E_G)=\exp\left[-\sqrt{E_G/E}\right]$$ Where I'm using the numerator $E_G$ as the ...
8
votes
4answers
701 views

Does Dirac's argument against classical mechanics stand in contradiction to Bohm's theory?

In his book on Quantum Mechanics, P.A.M. Dirac talks about the stability of the atom as a means of demonstrating the need for quantum mechanics. He writes: The necessity for a departure from ...
6
votes
1answer
180 views

How can I simulate a model electronic hole?

Suppose I can solve time-dependent Schrödinger equation for several 1D particles (currently 3). I'd like to see, what an electronic hole is and how it behaves — in a series of numerical experiments. ...
0
votes
1answer
75 views

Eigenstates of position and momentum operators in QM

In Griffiths pages 103-105 "Introduction to Quantum Mechanics" 2nd editiion he states that the eigenfunctions of the position and momentum operators are $$g_y(x) = \delta(x-y)$$ where the eigenvalue ...
5
votes
1answer
136 views

How to calculate the ground states' Berry phases with doubly degeneracy, such as that due to the particle-hole symmetry or time reversal symmetry?

Suppose the ground states of a system are doubly degenerate due to an anti-unitary symmetry $K$, which are $|\psi>$ and $|K\psi>$. If the system is an one-dimensional Fermion system and ...
2
votes
1answer
158 views

Para and ortho hydrogen angular momentum values

In Wikipedia, it is said that: Orthohydrogen, with symmetric nuclear spin functions, can only have rotational wavefunctions that are antisymmetric with respect to permutation of the two protons. ...
5
votes
2answers
133 views

Rigorous definition of density of states for continuous spectrum

For operators with pure point spectra it is clear how to count number of states corresponding to a given eigenvalue - one can just calculate the dimension of eigenspaces. I am wondering how to do it ...
-6
votes
0answers
38 views

What are Black holes exactly? [on hold]

A Black Hole is a very large rip in the atmosphere that opens after to many shuttles have traveled into space. It happens after about 5 million years of shuttles traveling in and out of spaces ...
0
votes
3answers
526 views

Quantum Mechanics in Electric Field

I am working on a problem which looks like this. Consider a charged particle with charge $q$ trapped in a box of length $L$ with finite constant potential $ V_0 $ on both ends. A constant (static) ...
5
votes
4answers
853 views

The Momentum Operator in QM

I've seen the 'derivation' as to why momentum is an operator, but I still don't buy it. Momentum has always been just a product $m{\bf v}$. Why should it now be an operator. Why can't we just multiply ...
3
votes
1answer
95 views
+50

In semiconductor devices, why is quantum tunneling “fast”?

I'm reading up on semiconductor devices that rely on quantum tunneling, such as the tunnel diode and the TFET. The big advantage of these devices is apparently that "quantum tunneling is extremely ...
1
vote
1answer
31 views

understanding thermal radiation in a conductor, gas and insulator

Context: I was in my bliss of ignorance and happiness when I was taught that quantum mechanics was about nice discrete values of energies. Now I am introduced the idea of Fermi Energy in a block of ...
54
votes
1answer
7k views

If we had a “perfectly efficient” computer and all the energy in the Milky-way available, what number could it count to?

The idea for this question comes from an example in cryptography, where supposedly 256-bit symmetric keys will be enough for all time to come (brute-forcing a 256-bit key is sort-of equivalent to ...
0
votes
1answer
43 views

Fermi energy of electron gas with electrostatic interaction

I have been given the following exam question and am unsure how I would go about solving it: Consider the case of a one-dimensional metal, consisting of a chain of $N$ positive charges $+q$ ...
1
vote
0answers
23 views

Stress testing Quantum Uncertainty, a multi Phase Question

I start this line of thinking i begin to seek the right questions to ask. I am of humble origin, but even here i remember that it all starts small somewhere. I think that even the greatest minds ...
0
votes
4answers
394 views

Heisenberg's uncertainty principle for electrons and atoms

Here is a video of Michio Kaku discussing Moore's Law and the quantum mechanical limits thereof. Around the 1:30 mark he's talking about how the chips today have a layer of 20 atoms across (I'm ...
0
votes
2answers
140 views

General formula for expanding wave function in terms of orthogonal states?

Given a wave function $\psi(x) = \langle \psi | x \rangle$. It can be expanded in terms of orthogonal states: $$ \langle \psi | x \rangle = \sum_n \langle \psi | n \rangle \langle n |x \rangle $$ ...
-12
votes
1answer
108 views

After proving that the photon remains stationary in the fourth dimension, must we conclude that the fourth dimension is moving at c? [on hold]

Firstoff, in his general relativity Einstein showed that dimensions could bend, curve, and move. This is an experimentally proven fact. Dimensions can, and do, move. In an earlier post we ...
3
votes
1answer
409 views

How does an operator transform under time reversal?

We know that a time-reversal operator $T$ can be represented as $$T=UK$$ where $U$ is some unitary operator and $K$ is the complex conjugation operator. Then under time-reversal operation, a quantum ...
0
votes
2answers
70 views

Variation of schrodinger cat replaced by quantum computer

In the "classical" imaginary Schrodinger's cat experiment, which seems to be no longer serious, or at least irrelevant, by many (some?) people, everything is explained away by decoherence. Now, let ...
1
vote
0answers
35 views

How to generalize the Bohr-Sommerfeld quantization condition to more dimensions?

As in the title-how to consider this condition on e.g. a polar or spherical coordinate system, with two or three dimensions? Which different methods I can use? EDIT: the coordinate system doesn't ...
6
votes
1answer
185 views

Uncertainty relation for non-simultaneous observation

Heisenberg's uncertainty relation in the Robertson-Schroedinger formulation is written as, $$\sigma_A^2 \sigma_B^2 \geq |\frac{1}{2} \langle\{\hat A, \hat B\}\rangle -\langle \hat A\rangle\langle ...
2
votes
1answer
116 views

How force get transmitted when a magnet attracts iron?

According to particle physics , every fundamental force has its force carrier particle. Photon is a force carrier particle of electromagnetic force but how does force gets transmitted when a iron is ...
4
votes
4answers
159 views

Is time an observable in Relativistic Quantum Mechanics?

Relativistic Quantum Mechanic is based, as far as I know, in the Dirac Equation. Now, the Schrödinger equation, in the abstract state space takes the form: $$i\hbar ...
0
votes
2answers
54 views

Atom Particles Relationships

I am an agriculture student, and we study tons of chemistry, and despite I took the exams I still have a good doubt on atoms. Through my studies I would say electrons are very tiny containers of ...
-2
votes
2answers
151 views

Would Einstein have accepted the presumptions that lead to the Bell inequality?

To check the correlation between Hidden Variable Theory and Quantum Mechanics, Bell calculated the expectation value $$<\sigma_{e}(\vec a,\vec V) \sigma_{p}(\vec b,\vec V)> = \int d^n V ...
0
votes
0answers
71 views

Parity operators and spin

Consider the following excerpt from Weinberg's Lectures on Quantum Mechanics: I follow everything up until the last statement in the excerpt. In fact, from other things I've read, it seems that one ...
0
votes
2answers
148 views

Does quantum randomness measurably affect macro-sized objects?

I understand that while it is believed that there is no true randomness on the macro scale, there is true randomness on the quantum scale. A previous theory that quantum processes could be determined ...
6
votes
2answers
69 views

Is there any atom which is dia-electric?

Take an atom. Suppose we impose some magnetic field on it. For some atoms, the energy increases---this is a phenomenon of diamagnetism. The question is, how about an electric field? Can the energy ...
8
votes
1answer
222 views

Delocalization in the square root version of Klein-Gordon equation

In this Wikipedia article a relativistic wave equation is derived using the Hamiltonian $$H=\sqrt{\textbf{p}^2 c^2 + m^2 c^4}$$ Substituting this into the Schrödinger equation gives the square root ...
2
votes
0answers
69 views

Analyzing the free-particle kernel [closed]

I recently began studying the theory of path integrals from the book by Feynman and Hibbs. The Problem $3.6$ asks to give an argument to show that $F(t_b,t_a)$ depends only on $t_b-t_a$. ...
0
votes
2answers
103 views

Are electron densities and electrostatic forces possibly responsible for gravity? [closed]

The idea I had was that whilst electrons usually orbit within the Bohr radius of atoms there is a chance of them appearing significantly further away than that, meaning that if all the electrons in ...
3
votes
1answer
135 views

Sequential Stern-Gerlach devices - realizable experiment or teaching aid?

At least one textbook [1] uses sequential Stern-Gerlach devices to introduce to students that the components of angular momentum are incompatible observables. Viz., the $z$-up beam from a SG device ...
1
vote
0answers
41 views

Does anyone know how/where I could view the Double slit experiment in person? [closed]

I want to see the double slit experiment in person! The one where the observer effects the wave/particle state of an electron. Where would I be able to view this experiment? Is it on display in any ...
6
votes
1answer
143 views

Question on doing the integral for Fermi golden rule

Today in the lecture, my professor did something which confused me As an example, we consider the photoelectric effect, in which an electron bound in a Coulomb potential is ionized after ...
2
votes
3answers
107 views

Would a particle the size of a neutron, if it had enough mass, collapse into a blackhole?

For example, a neutron is a particle that occupies a certain volume. If you pack enough mass into that volume, it would collapse into a black hole (I assume there is not enough mass now). At least if ...
1
vote
2answers
383 views

What is the significance of Fermi temperature?

The Fermi temperature of a solid is related to Fermi energy by relation $$ { E }_{ F } ={ k }_{ B }\times{ T }_{ F } $$ where $ { k }_{ B } $ is Boltzman constant. But what is the significance of ...
17
votes
4answers
2k views

What is a wave function in simple language?

In my textbook it is given that 'The wave function describes the position and state of the electron and its square gives the probability density of electrons.' Can someone give me a very ...
1
vote
1answer
37 views

Why can one suppose $\alpha^i$ and $\beta$ matrices in the derivation of the Dirac Equation?

On the derivation of the Dirac Equation one usually supposes that it is possible to write $$E = \mathbf{\alpha}\cdot \mathbf{p} + \beta m.$$ One then deduces that in order to have $E^2 = p^2+m^2$ it ...
0
votes
0answers
44 views

Local Phase Transformation of the Dirac equation

The Dirac Equation ("free Dirac") is a relativistic Equation of Motion (EoM) for a free ($V=0$) Spin $1/2$ particle (like an electron). The free Dirac equation is invariant under global phase ...