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
2answers
196 views

What will happen if a ground state hydrogen atom is placed in a low frequency, but high intensity laser field?

Similar questions have been asked before, but this one extends the scope of interpretation and applications. Let us ask the question: What will happen if we have a laser gun that produces a high ...
13
votes
6answers
3k views

What is $\Delta t$ in the time-energy uncertainty principle?

In non-relativistic QM, the $\Delta E$ in the time-energy uncertainty principle is the limiting standard deviation of the set of energy measurements of $n$ identically prepared systems as $n$ goes to ...
2
votes
2answers
1k views

Changes in Water Bonding Angle

I heard something recently in a casual discussion, but have yet to be able to confirm it: is there any evidence that the bonding angle for a water molecule, currently defined as 104.5, has been either ...
3
votes
1answer
2k views

What happens if an atom absorbs a photon of energy higher than first excited state but lower than second excited state? [duplicate]

Since the energy levels of atoms are quantized, I was wondering what happens if an electron is hit by a photon whose energy is higher than electron's first excited state but lower than second excited ...
5
votes
1answer
131 views

Tracing out an observable vs integrating over unitaries

Let $O$ be an observable on a Hilbert space $\mathcal{H}$, and let $B$ be a subset of the spins composing $\mathcal{H}$, and let $\bar{B}$ be its complement. Now define $\displaystyle O_B = ...
9
votes
1answer
388 views

How fat is Feynman’s photon?

According to my calculations, it is a lot skinnier than Airy’s photon, but still a whole lot fatter than a straight line. So, how does a photon get from point A to Point B? The ray optics ...
1
vote
1answer
104 views

Photon indistinguishability and beam splitters

$\newcommand{\bra}[1]{\left\langle#1\right|}$ $\newcommand{\ket}[1]{\left|#1\right\rangle}$ Suppose I have a beam splitter that will either reflect a photon by 45 degrees, or will allow the photon to ...
5
votes
2answers
1k views

Pauli matrix rotations

When doing physics with two-level systems and introducing rotations, a term that appears quite often is the rotation of a Pauli matrix by another one: $$e^{- i \sigma_j \theta/2} \sigma_k e^{i ...
4
votes
4answers
4k views

Confused over complex representation of the wave

My quantum mechanics textbook says that the following is a representation of a wave traveling in the +$x$ direction:$$\Psi(x,t)=Ae^{i\left(kx-\omega t\right)}\tag1$$ I'm having trouble visualizing ...
10
votes
1answer
334 views

Nuclear Magnetic Resonance (NMR) Conceptual Questions

Let $M$ be the magnetic moment of a system. Below are the Bloch equations, including the relaxation terms. $$\frac{\partial M_x}{\partial t}=({\bf M} \times \gamma {\bf H_0})_x-\frac{M_x}{T_2} $$ ...
5
votes
3answers
784 views

Particle coming across a step potential barrier

My quantum mechanics textbook says that when a particle (in the classical case) comes across a potential-step barrier of finite height, if it has sufficient energy to surmount the barrier, it will ...
1
vote
1answer
146 views

Constant-dependent potential in radial Schrodinger equation

Studying quantum mechanics, I've found an exercise I don't know how to solve it. Given the radial Schrödinger equation, $$\left [ \frac{d^2}{dr^2}+k^2-\frac{2m}{\hbar^2}\lambda U\left ( r \right ) ...
1
vote
1answer
400 views

What's the average position of oscillating particles in a box with periodic boundary conditions?

Imagine an open box repeating itself in a way that a if a particle crossing one of the box boundary is "teleported" on the opposite boundary (typical periodic boundary position in 3D). Now put a ...
0
votes
1answer
227 views

Quantum entanglement, quantum measurement, spin and position

By uncertainty principle, we know that determining particle's position at some location is limited. So we cannot determine the position of a particle at some exact point location as this would make ...
9
votes
2answers
629 views

Has The Aharonov-Bohm Effect Been Experimentally Proven?

I have encountered two contradicting papers on the Aharonov-Bohm Effect: One supporting, The Aharonov-Bohm Effects: Variations on a Subtle Theme. H Batelaan and A Tonomura. Physics Today 62 pp. ...
0
votes
1answer
666 views

Solving the 1-D Schrodinger equation for a free particle: Confused about 2 possible general solutions

I am following Griffiths' Introduction to Quantum Mechanics, as well as an online lecture that follows a different book, and both sources give different equations for the general solution of the 1-D ...
1
vote
2answers
110 views

Given a state function of a particle, can we determine its mass?

The quantum state of a system is supposed to contain all the information that can be obtained about the system such as its energy, momentum...etc. So I have 2 questions: 1-If someone gave us a ...
1
vote
1answer
363 views

Quantum Ripples?

Would someone please explain what quantum ripples are? I've heard of gravitational waves, are they the same thing? I overheard someone saying that it could allow for possible faster than light speed ...
3
votes
2answers
450 views

How do particles, such as electrons become visible?

Quantum mechanics says that atoms are invisible - they do not have some specified location, only a probability distribution. So, how can we see them? If there is to be particle-antiparticle ...
1
vote
1answer
121 views

Data For Quantum Entanglement

Is there any publicly accessible data that shows quantum entanglement empirically. I want to see what these researches are seeing that is showing them that indeed this phenomenon is real. Also, any ...
6
votes
2answers
951 views

Amplitude of Probability amplitude. Which one is it?

QM begins with a Born's rule which states that probability $P$ is equal to a modulus square of probability amplitude $\psi$: $$P = \left|\psi\right|^2.$$ If I write down a wave function like this ...
2
votes
0answers
299 views

Probability and probability amplitude [duplicate]

What made scientists believe that we should calculate probability $P$ as the $P = \left|\psi\right|^2$ in quantum mechanics? Was it the double slit experiment? How? Is there anywhere in the ...
2
votes
1answer
2k views

Solving the time independent Schrodinger equation: Does a complex solution make sense?

In my notes, I have the Time Independent Schrodinger equation for a free particle $$\frac{\partial^2 \psi}{\partial x^2}+\frac{p^2}{\hbar^2}\psi=0\tag1$$ The solution to this is given, in my notes, ...
12
votes
2answers
930 views

Dimension of Dirac $\gamma$ matrices

While studying the Dirac equation, I came across this enigmatic passage on p. 551 in From Classical to Quantum Mechanics by G. Esposito, G. Marmo, G. Sudarshan regarding the $\gamma$ matrices: ...
1
vote
1answer
122 views

The status / acceptance of block time?

What is the current status or acceptance of block time as it relates to Einstein's theory of relativity? Has quantum mechanics ruled it out or is it still the favored view of the world? Perhaps there ...
3
votes
3answers
3k views

Matrix elements of momentum operator in position representation

I have two related questions on the representation of the momentum operator in the position basis. The action of the momentum operator on a wave function is to derive it: $$\hat{p} ...
5
votes
1answer
300 views

Why is the Wick contraction in HFB or BCS equal to a single-particle density?

I'm trying to understand how in Hartree-Fock-Bogoliubov (HFB) or BCS theory we can write a product of creation/annihilation operators as single-particle densities under the guise of "Wick's theorem". ...
2
votes
1answer
522 views

What is the mathematical background needed for quantum physics? [duplicate]

I'm a computer scientist with a huge interest in mathematics. I have also recently started to develop some interest about quantum mechanics and quantum field theory. Assuming some knowledge in the ...
2
votes
1answer
813 views

Minimal Kinetic energy for particle in a box

This is driving me crazy! The question goes as follows: A proton is enclosed in a zone of length 2pm along the x-axis. The minimal kinetic energy of the proton lies closest to: 5000eV 0.5eV 50eV ...
1
vote
0answers
2k views

How is multiplicity given by 2S+1?

Suppose there are two electrons in an atom with $s_1 = \frac{1}{2}$, $l_1 = 1$ and $s_2 = \frac{1}{2}$, $l_2 = 1$. Hence the total $S$ (of the atom) may be +1 or 0. And total $L$ is either $+2$, $+1$ ...
5
votes
1answer
413 views

Born-Oppenheimer separation in Dirac bra-ket notation

Most derivations I have seen of the Born-Oppenheimer approximation are made using wave-functions. To understand it better, I was trying to write a derivation using Dirac notation, but I am stuck. I am ...
4
votes
2answers
856 views

When and how did the idea of the tensor product originate in the history quantum mechanics?

At some point in the history of quantum mechanics, it was accepted that a single particle is described by a wavefunction which is a function of the position of the particle $\mathbf{r}$, denoted: ...
2
votes
1answer
822 views

Can silicon droplets bouncing on a vibrating surface be a model for Quantum Mechanics?

In this video on youtube it is claimed that silicon droplets bouncing on a vibrating surface show behaviour in analogy to particle/wave duality in Quantum Mechanics. Is this true? Did they ...
3
votes
1answer
182 views

Born Oppenheimer Approximation: Why can any molecular state be represented as a linearcombination of electronic states?

in the Born Oppenehimer Approximation, one expands the molecular wavefunction $\Psi(x,X)$ in terms of the electronic wavefunctions $\phi(x;X)$: $\Psi(x,X)$ = $ \sum_k(c(X)_k\phi(x;X)_k)$ (x are the ...
2
votes
0answers
47 views

Why the peak of spectrum gets vague when the dimension is lower?

In a many-body system, we can know the spectrum function at a particular temperature from Green function. It means density of states. A peak of spectrum represents one mode. My question is that in the ...
2
votes
2answers
375 views

How can electrons be confined in Quantum dots?

Atoms are in the range of $1$ Angstrom while Quantum dots are in the range of $2$-$10$ nm. In any atom, $99.9$% is unoccupied. So if I have a Quantum dots of size $3$ nm and suppose in my Quantum dot, ...
2
votes
2answers
408 views

What are the “loopholes” in past Bell's theorem experiments?

I am intrigued by the following Phys.org article: Researchers began using photons in 1980s to test Bell's theory and determine if Einstein's reasoning is right or wrong. Since then, researchers ...
2
votes
2answers
321 views

Charged quantum particle in a magnetic field - choosing a different gauge leads to different wavefunctions

Consider a charged quantum particle confined to the $xy$ plane, subject to a magnetic field $\mathbf{B}=B\hat{z}$. The Hamiltonian is: $$ H = \frac{1}{2m} \left( \mathbf{p} - \frac{e ...
0
votes
1answer
1k views

Infinite square well in momentum space

As we know the eigenfunctions for a particle of mass m in an infinite square well defined by $V(x) = 0$ if $0 \leq x \leq a$ and $V(x) = \infty$ otherwise are: $\psi_n (x) = \sqrt{(2/a)} sin(n \pi ...
2
votes
2answers
3k views

Particle in infinite potential well which is doubled in size at $t_0$

I am currently studying for an exam in Quantum Mechanics and came across a solution to a problem I have trouble with understanding. The Problem: A Particle sits in an infinite potential well ...
2
votes
2answers
131 views

How should I simulate the electric potential field from a wavefunction?

I was interested in making what I thought would be a simple simulation of an electron encountering a positron by numerically solving the Schrodinger equation over several time steps, but I've run ...
0
votes
0answers
68 views

What exactly is the spin of a particle? [duplicate]

Possible Duplicate: What is spin as it relates to subatomic particles? I'm having a hard time grasping the concept of spin, my textbook describes it very vaguely: Stable matter contains ...
3
votes
1answer
550 views

Expectation values-Wavefunction

I'm a bit puzzled about an excercise in which I have to find the expectation values for position and momentum. Normally this should be pretty easy but in this case I just don't get the point. ...
1
vote
3answers
2k views

Partition function for quantum harmonic oscillator

Hi guys I'm currently trying to solve a mock exam for an exam in a few days and am a bit confused by the solutions they gave us for this exercise: Exercise: A solid is composed of N atoms which ...
8
votes
2answers
195 views

Could an ultra-relativistic particle tunnel directly through a stellar mass black hole?

It occurred to me in passing that the Lorentz contraction of a black hole from the perspective of an ultra-relativistic (Lorentz factor larger than about 10^16) particle could reduce the thickness of ...
2
votes
2answers
754 views

Constructing the exponential form of a unitary operator

I think I've got this figured out but wanted to make sure I'm doing this right. Working with operators that satisfy bosonic commutation relations $[b,b^\dagger] = 1$, I define a very general unitary ...
1
vote
1answer
827 views

Is the Pauli exclusion principle as Brian Cox described it? [duplicate]

Possible Duplicate: Does the Pauli exclusion principle instantaneously affect distant electrons? If this rule works, could you not set up an experiment to test the theory (as described by ...
0
votes
1answer
721 views

How do I find the eigenvalues for the angular momentum ladder operators?

I am trying to calculate the normalising constants for the angular momentum ladder operators but am stuck when I need to calculate expected values. How can I find the expected values
1
vote
1answer
140 views

What do the $j$ and $m$ stand for in $|j,m\rangle$ for angular momentum in quantum mechanics?

I'm assuming it is a jth state with m value as total angular momentum?
1
vote
1answer
3k views

Deriving group velocity

At the introduction to quantum mechanic phase $v_p$ and group $v_g$ velocities are often presented. I know how to derive $v_p$ and get equation: $$ \scriptsize v_p=\frac{\omega}{k} $$ What i dont ...