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 (3)

0
votes
2answers
48 views

Experimentally, what categorizes a measurement as corresponding to a certain observable?

I want to write a computer program. The input to the program is: A description of an experimental device (for instance a Stern-Gerlach apparatus, or a laser and a polarizer) What the experimenter ...
0
votes
1answer
39 views

Probability of superimposed states vs probability of separate states

Suppose there is an infinite square well where $\psi_1$ and $\psi_2$ are the ground state ($n=1$) and the first excited state ($n=2$), and each satisfies the time-independent Schrodinger equation. ...
1
vote
1answer
49 views

Lorentz Invariance of the Dirac equation

My question is more conceptual than mathematical. As a differential equation the Dirac equation is invariant under Lorentz transformations. Conceptually though Lorentz transformations describe a ...
-2
votes
2answers
61 views

problem with learning Quantum Mechanics [on hold]

I've started learning quantum Mechanics from " Griffiths " book and finished chapter one , but the problem is i feel most of what i'm doing is mathematics , for example he solved the problem of ...
5
votes
3answers
103 views

How do we know that the Fourier transform of space is momentum?

How do we know that the Fourier transform of real space $x$ is the momentum $p$ space or for energy and time, receptively? What's the mathematical process and physical logic?
1
vote
2answers
109 views

Eigenvalues being physical observables

I think I'm comfortable with the PDE solutions to the Schrodinger equation. But as soon as we start putting these values in a matrix (in dirac notation), I lose my understanding and everything ...
3
votes
2answers
528 views

Proving that $i\hbar\frac{\partial}{\partial \mathbf{p}}$ is the operator of $\mathbf{x}$ in momentum space

How can I prove that $i\hbar\frac{\partial}{\partial \mathbf{p}}$ is the operator of $\mathbf{x}$ in momentum space?
1
vote
3answers
145 views

Measurement of quantum state

Consider a particle in a box system.Assume its state to be a superposition of the ground and the first excited energy states.Consider two observers A and B (rest of the world).A made the measurement ...
16
votes
1answer
797 views

Intuitive meaning of Hilbert Space formalism

I am totally confused about the Hilbert Space formalism of Quantum Mechanics. Can somebody please elaborate on the following points: The observables are given by self-adjoint operators on the ...
0
votes
0answers
44 views

Do twice more atoms absorb twice more photons?

Let's assume you have a photon detector that detect individual photons striking it when exposed to a weak light source. Now let's assume you somehow managed to make a denser detector from the same ...
1
vote
0answers
60 views

A conceptual question about scattering theory in quantum mechanics

When defining the cross section, we use this formula $$ \psi_S = \frac{f(\theta,\phi)}{r} e^{ikr},$$ to prove this one $$ j_{out} = \frac{|f(\theta,\phi)|^2}{r^2} \frac{\hbar k}{\mu},$$ and then ...
0
votes
0answers
14 views

How to derive the electron dipole selection rule in coupled bases?

We need to find $| \psi_f \rangle$ fulfilling the condition that $$ | \langle \psi_f | \mathbf{x} | \psi_i \rangle |^2 \neq 0.$$ When using the uncoupled bases $| l,m,m_s \rangle$ I can derive the ...
3
votes
1answer
88 views

Half integer eigenvalues of orbital angular momentum

Why do we exclude half integer values of the orbital angular momentum? It's clear for me that an angular momentum operator can only have integer values or half-integer values. However, it's not clear ...
1
vote
2answers
123 views

Understanding basic quantum mechanics notation

I was talking with a guy about energy levels of an atom in a magnetic field. He said that energy levels are shifted and that, if you want know how much, you have to analyze this: for 1s state: ...
1
vote
3answers
73 views

Two-Particle System

I thought that the general composite wave function for Identical Bosons is: \begin{equation}\label{} \psi_{+}(r_1,r_2)=A[\psi_{a}(r_1)\psi_b(r_2)+\psi_b(r_1)\psi_a(r_2)] \end{equation} but I stumbled ...
3
votes
5answers
187 views

How does a Wavefunction collapse?

I have been wondering and researching... How does a wavefunction collapse into one state?More specifically, what conditions cause a wavefunction for a quantum particle to collapse? Does this have to ...
3
votes
0answers
37 views

Cubic perturbation to coupled quantum harmonic oscillators

I recently came across this two-dimensional problem of a particle in a potential of the form $$V = \displaystyle{\frac{1}{2}m \omega^2} \big(y^2 + x^2y \big) - \alpha y,$$ where $x$ and $y$ are known ...
2
votes
2answers
151 views

When do we see particles to be in a superposition of energy states?

I have two doubts: Exactly when does this happen? and If we are in a superposition of states (lets say E1 and E2) and the particle absorbs a photon, what will happen? If E3-E1 = hf, will it go to E3? ...
1
vote
3answers
55 views

For the Uncertainty Principle, Do the Units of the Two Complementary Quantities have to Equal Js?

I know that the Uncertainty Principle is: $△P•△Q=ħ/2$. But do the units on the Left Hand Side of the equation always have to equal 'Js', i.e. Energy x Time (the same is the Plank Constant, $h$) or is ...
1
vote
0answers
26 views

How does Dirac define the representative of $\{\langle\phi\frac{d}{dq}\}\psi\rangle = \langle\phi\{\frac{d}{dq}\psi\rangle\}$

On pate 89 of Dirac's book, The Principles of Quantum Mechanics, he writes: Let us treat the linear operator $\frac{d}{dq}$ according to the general theory of linear operators of section 7. We ...
4
votes
3answers
877 views

$\hbar$, the angular momentum and the action

Is there anything interesting to say about the fact that $\hbar$, the angular momentum and the action have the same units or is it a pure coincidence?
-3
votes
1answer
57 views

probability amplitude and path integrals [on hold]

Recently, I have been learning about path integrals and I was wondering, can the probability of a certain path be weighted more in a path integral? Said in another way, can certain paths have more ...
15
votes
5answers
2k views

How does the concept of a “black body” make any sense?

In my introductory chemistry class, we are learning about the basics of quantum mechanics. We were introduced to the concept of emission and absorption spectra. Our textbook describes how electrons ...
1
vote
1answer
58 views

What are observables? [on hold]

What are observables and how are they related to quantum decoherence and wavefunction collapse. I read this: Observables - what are they? but it was about the technical details on observables. Even ...
6
votes
3answers
316 views

How would a realist interpretation of the Mermin-Peres square look like?

How would a realist interpretation of the Mermin-Peres square with counterfactual definiteness and the existence of states prior to measurements look like?
5
votes
1answer
79 views

Equivalence classes in a Hilbert space

I'm reading something about quantum information/quantum computing theory, and I've run into a wall. I know what is meant by an equivalence class and how something can be partitioned into equivalence ...
1
vote
2answers
57 views

Proof that quantum Fourier transform is unitary

I'm trying to work through the proof that the quantum Fourier transform can be described by a unitary operator, i.e $F^{\dagger}F=\mathbb{1}$, where ...
4
votes
4answers
189 views

What does observation mean in two-slit electron diffraction experiment? [duplicate]

My question is clear, that I ask: What do we mean by "observation" in 2-slit experiment for electrons (or any other wave-particle)? You know, we say that :"if we observe the electron, it shows a ...
2
votes
3answers
298 views

Plants and Quantum Mechanics!

So, I have been working on quantum biology and found something interesting that I would like to write an equation for: Scientists have wondered how plants have such a high efficiency in ...
0
votes
1answer
62 views

Bound States in quantum mechanics [on hold]

A particle is found in the following potential: $$V(x)=\infty \quad \text{for} \quad x<0;$$ $$V(x) = -V_0 \quad \text{for} \quad 0<x<a;$$ $$V(x) = 0 \quad \text{for} \quad x>a.$$ Given ...
0
votes
1answer
85 views

Electron at rest

David Griffiths suggested a website in his book where I got this paper http://www.hep.princeton.edu/~mcdonald/examples/electronatrest.pdf Here the author says classically a particle at rest(in some ...
1
vote
1answer
52 views

using a given wavefunction to find particle properties

Let's say we have a given wavefunction and we want to find a particle that will fulfill the properties for that wavefunction. How can we do that? Is it possible? I was thinking of using Schrodinger's ...
0
votes
0answers
24 views

Double well potential [on hold]

A particle is in the following double-well potential with $E<0$: $$V(x)=0 \quad for \quad x<-a, x>a; -V_0 \quad for \quad -a<x<-b, b<x<a; 0 \quad for \quad -b<x<b$$ I am ...
0
votes
1answer
58 views

Perturbations in arbitrary dimensions

In general is it acceptable to say that if a perturbation is in only one spatial direction then the energy eigenvalue to second order is only changed in that spatial direction? For example 3D ...
1
vote
2answers
426 views

Coupled Quantum Harmonic Oscillator

Given the following Hamiltonian for two identical linear oscillators with spring constant $k$ and interaction potential $\alpha x_1x_2$; I was asked to find the expectation value $\langle ...
0
votes
0answers
26 views

Why spin-$\frac{1}{2}$ nuclei have zero electric quadrupole moment?

Why spin-$\frac{1}{2}$ nuclei have zero electric quadrupole moment? How to calculate in general?
2
votes
1answer
28 views

How does inflation relate to spontaneous matter creation?

According to Inflation for Beginners, ... quantum physics allows the entire Universe to appear, in this supercompact form, out of nothing at all, as a cosmic free lunch. The idea that the Universe ...
0
votes
2answers
40 views

How to connect Rabi frequency with absorption intensity?

If a particle with non-degenerate spectrum starts in some eigenstate, and the frequency of the external EM field matches some transition frequency, then this would lead the particle to do periodic ...
-4
votes
6answers
2k views

Why won't protons revolve around the nucleus containing electrons and neutrons?

In case of solar system,we can explain "Why Sun would not revolve around any other planet?",by giving the reason that Sun is heavier than any other planets. Heavier the body,greater will be the ...
-4
votes
2answers
582 views

What really is the smallest “mass” or “object” in the universe?

Look at this here. With respect to the sciences, the atom is obviously not the smallest piece of mass. Apparently, if people have already broken down the atom in to particles smaller than so, why ...
-8
votes
1answer
106 views

Does Anything Exixts? [closed]

I Mean that Does Anything In The Universe Exists By Means Of Quantum Mechanics...I Heard This From Someone But i wanna be sure that it is really true or what?.
-11
votes
2answers
257 views

if the universe is flat does it mean it exists only in our mind as math? [closed]

My dad, who is a retired mathematician, has this attitude, which I think we all have as kids, that ultimately reality is made of stuff. End of story. If you look around yourself in the world, ...
9
votes
3answers
564 views

How to motivate Schrödinger's Equation? [duplicate]

Schrödinger's equation is supposed to be a differential equation for the wave function of a particle. As I currently understand, De Broglie's hypothesis is a hypothesis that for particles there should ...
2
votes
1answer
34 views

How are momentum and position operators dependent on the chosen inertial frame?

How are momentum and position operators in quantum mechanics dependent on the chosen inertial frame of reference?
1
vote
2answers
95 views

Need of vector potential in quantum mechanics

I need your opinions. Why is the vector potential of a magnetic field important (or even necessary) to quantum mechanics? Why it has to be defined everywhere? Is there any fundamental reason you can ...
3
votes
1answer
172 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 ...
0
votes
2answers
104 views

Quantised Angular Momentum?

So when learning about the Bohr model of hydrogen and de Broglie waves, it was shown that treating the electron of hydrogen as a de Broglie wave results in the relationship $$L=n\hbar, \qquad ...
3
votes
1answer
66 views

Why according to Hund's first rule all electron with same spin should occupy orbitals when partially filling?

I get that because of coulomb repulsion initially all the electrons will not occupy the same site but will single occupy the orbitals.But while doing so how do they know to keep their spins aligned ...
0
votes
5answers
133 views

The meaning of Superposition

Is superposition purely conceptual or does it represent some real "thing"? Said another way, is superposition thought to have some tangible physical manifestation or is it simply the lack of physical ...
2
votes
1answer
75 views

Eigenfunctions of Schrodinger equation

Why the solutions of the Schrodinger equation are called the eigenfunctions? For an electron moving in one dimensional lattice the eigenfunctions are given by$$\psi(x)=u_k(x)e^{ikx}.$$