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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What is the electric field outside a cylindrical solenoid?

What is the electric field outside a cylindrical solenoid when inside is turned on a magnetic field? The question is related to the question aharonov-bohm-effect-electricity-generation
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why does muon hop rate in metals change with temperature like this

you can find this figure in this pdf we use μSR to study the superconductor properties,,but I don't quite understand the T^-9 slope, does muon trapped in an interstitial site and hop rate drop with ...
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39 views

How to compute observables from the boson field operator? [on hold]

I think I understand that if given the two boson wavefunction of two different states \begin{align} \Psi(\boldsymbol{r}_1,\boldsymbol{r}_2) = \dfrac{ \psi_1(\boldsymbol{r}_1)\psi_2(\boldsymbol{r}_2) + ...
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2answers
38 views

Why angular momentum about three independent axes?

The generic commutation relations for the angular momentum operator are $[J_x, J_y] = i \hbar J_z$, where the $J_i$, $i = x,y,z$ are the components of the angular momentum vector operator, $\mathbf ...
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1answer
37 views

Connection to spin 1/2 electron system?

In another Physics stack exchange thread here, Spin matrix for various spacetime fields I obtained the generator of rotations of the SO(2) rotation group for an infinitesimal rotation of 2D vectors. ...
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26 views

How to derive equation for probability current density in relativistic quantum mechanics [on hold]

How does one derive equation for probability current density in relativistic quantum mechanics? I am asking for textbook-styled explicit derivation. No need for any other background knowledge.
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1answer
63 views

Are operators in quantum mechanics linear transformations?

Observables in quantum mechanics correspond to self-adjoint linear operators. If $\psi$ is an eigenvector of $\hat A$, then $\hat A\psi=\alpha\psi$ where $\alpha$ is the eigenvalue of $\psi$. ...
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65 views

Expanding a ket in the position basis?

My textbook says that to find the ket $|ψ\rangle$ in the same position basis as the ket $|ø\rangle$ we do the following: $$|ψ\rangle=\int dø|ø\rangle \langle ø|ψ\rangle$$ Firstly can $|ø\rangle$ be ...
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30 views

Spontaneous breaking of a discrete non-Abelian symmetry

Can someone give an example of an one dimensional local gapped quantum lattice model with a discrete non-Abelian global internal symmetry that is spontaneously broken in the ground state? In ...
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46 views

Complete description of two electrons with spin

We have two electrons described by the wave function $\phi(\vec{x}_1,\vec{x}_2,s_1,s_2;t)$ where $\left| \phi(t)\right\rangle$ is the state vector and $(\vec{x}_1,\vec{x}_2,s_1,s_2)$ is the index of ...
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1answer
33 views

Fock matrix elements for RHF formalism

Here I refer to a particular book Molecular Quantum Mechanics by Peter W. Atkins and Ronald S. Friedman, but similar derivation could be found in many other texts. So, when obtaining the explicit ...
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2answers
39 views

Do randomness and indeterminacy in Quantum Physics mean the same?

I have been trying to learn about the randomness in Quantum Physics. But of the many sources I referred to, some say about "Randomness in Quantum physics" and some others say about "Quantum ...
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1answer
66 views

The Eigenstate Existence Problem in Dirac's 'Principles of Quantum Mechanics'

In Chapter II of Dirac's Principles of Quantum Mechanics, Dirac explains that in general it is very difficult to know whether, for a given real linear operator, that any eigenvalues/eigenvectors exist ...
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2answers
100 views

What is the analogy of $|x\rangle$ in quantum field theory?

Let me start from path integral formulation in quantum mechanics and quantum field theory. In QM, we have $$ U(x_b,x_a;T) = \langle x_b | U(T) |x_a \rangle= \int \mathcal{D}q e^{iS} \tag{1} $$ ...
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25 views

Aharonov-Bohm Effect electricity generation

This question is based on highly intuitive picture of the Aharonov-Bohm effect (perhaps a naive one). From what I have read, the current explanation of the AB effect is that although the electron ...
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1answer
31 views

Solving particle on a ring problem using momentum eigenvalue equation instead of energy eigenvalue equation

I have read somewhere that for particle on a ring problem you don't have to solve eigenvalue equation $H\psi=E\psi$ you can instead solve eigenvalue equation $P\psi=p\psi$ where P is momentum ...
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1answer
47 views

How can we “know” that system interacted with another system or environment in quantum mechanics/decoherence?

I might be raising measurement problem in quantum physics in different words, but I will ask the question. Quantum decoherence has been proposed by proponents as a theory that eliminates all weird ...
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4answers
128 views

If wavefunction is just a probability function, how does an electron interfere with itself

I have read lots of quantum mechanics books. The chapters that are talking about De Broglie, lots of them name the chapter as "Wave-particle duality" and says: "Electrons are both waves and ...
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2answers
59 views

Estimating the radius of the Hydrogen atom

I've seen people estimate the Bohr radius using the uncertainty principle by assuming that $$\Delta x \sim r$$ and $$\Delta p \sim p$$ then $$p \approx \frac{\hbar}{r}$$ Using this assumption will ...
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2answers
77 views

Given eigenvalues of $\vec l^2$ and $\vec s^2$, calculate the eigenvalue for $\vec j^2$

There was an exam question that read approximatly: Let $\vec j = \vec l + \vec s$. Given eigenvalues of $\vec l^2$ and $\vec s^2$, calculate the eigenvalue for $\vec j^2$. We came up with $$\vec ...
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1answer
47 views

What are the proper domains of the position and squared angular momentum operator?

I am looking at the position operator on a compact set $K \subset \mathbb{R}^n$ and the squared angular momentum operator (so essentially the Laplace-Beltrami operator where I just look at the angular ...
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62 views

How should a math undergrad student prepare himself to study GR and QM? [duplicate]

I'm quite sure that similar questions like this have been asked for more than thousands of times on here but since each person's background and interests are unique I believe questions like this ...
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68 views

Instantons in Witten's supersymmetry and Morse theory

I'm reading Witten's paper on supersymmetry and Morse theory and am confused about the details of the instanton calculation which he uses to define a Morse complex (beginning at page 11 of the pdf) . ...
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4answers
438 views

Is the potential in Schrödinger equation an operator?

In the Schrödinger equation in the position representation $$ i\hbar\frac{\partial}{\partial t}\Psi(x,t) ~=~[\frac{-\hbar^2}{2m}\nabla^2+V(x,t)]\Psi(x,t), $$ is the potential $V(x,t)$ an operator ...
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1answer
86 views

My basis set isn't orthonormal?

I'm implementing a little QM calculation just for fun and to make sure I understand how it works (calculating the helium ground state energy). My problem is that my basis set doesn't seem to be ...
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1answer
83 views

Is there an absolute minimum scale to the universe? If so, why?

Based on my rather circumscribed understanding of modern physics, one of the key insights of quantum mechanics over previous scientific theories is the prediction that there exists an absolute limit ...
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41 views

Features used in quantum mechanics but not used in classical mechanics [duplicate]

What are (and why?) all the variables (features) used in the models in quantum mechanics but not used in classical mechanics (e.g. spin, flavor)?
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73 views

Does “dark matter” explain how I can have -1 apples? [on hold]

If I have 3 apples and you take 4 of them, that means I have -1 apples... is that apple made of dark matter?
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34 views

Non-unqiue basis sets of reduced density matrix in quantum mechanics/decoherence

In Why decoherence solves the measurement problem by Art Hobson: $|\psi \rangle _{SA} = c_1|s_1 \rangle |a_1 \rangle + c_2 |s_2\rangle |a_2 \rangle$ which is a wavefunction that describes non-local ...
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3answers
65 views

Differences between wavefunction, probability and probability density?

I am trying to understand the differences between wavefunction, probability and probability density. There are different definitions on the internet. For example: ...
2
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2answers
82 views

Interpretation of a density matrix as an observable

In quantum mechanics, any density matrix (or density operator) is Hermitian. Observables are also represented by Hermitian operators. So it follows that a density matrix can also be interpreted as ...
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48 views

Introductory derivations of Heisenberg uncertainty principle

I'm not an expert when it comes to quantum mechanics, so correct me wherever I'm wrong, but: I've always been a little bit bothered by introductory derivations of the Heisenberg uncertainty relations ...
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21 views

States that Wave-length, Pressure and Temperature describe [closed]

I have two doubts : 1 - Can wave-length of light emited by some light-source ( like a black-body ) take arbitrary distance values ( any value in the set of real numbers ) ? 2 - Pressure is the name ...
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45 views

Uncertainty principle implies the non-deterministic universe? [duplicate]

Does the uncertainty principle imply the non-deterministic universe, or just the fact that our model of the universe, the one based on observation, can be at most non-deterministic, since we will not ...
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1answer
55 views

Two related questions about double-slit experiments moving at a relativistic speed

I was wondering as how would appear the interference pattern of a double-slit experiment moving at a relativistic speed v, 1) in the case of light and, 2) in the case wave matter (i.e. electrons for ...
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1answer
108 views

What is the complete quantum description of a free electron

Basically, what are all the parameters that completely describe an electron in quantum theory. In classical physics a complete and fundamental description of an electron is given by its mass, charge, ...
1
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1answer
85 views

Has the photon both gravitational and inertial mass?

The theory of relativity shows that the inertial mass of a body increases with the energy it contains; if the increase of energy amounts to $E$, the increase in inertial mass is equal to $E/c^2$, ...
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32 views

Quantum computing implications [closed]

This May a canadian company has begun preliminary leasing on a first generation Quantum computer. I wanted to ask if any community members have come across any articles on how quantum computing may ...
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4answers
139 views

I don't get band structure of solids

If the energy levels of bound electrons are discrete, why do band structures in solids arise?
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3answers
292 views

Basis in quantum mechanics

My quantum mechanics textbook (Primer of Quantum Mechanics, by Marvin Chester) says that both the momentum space and the position space are basis spaces. It also says that the momentum space is ...
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19 views

matrix elements of the electronic molecular Hamiltonian between a hartree product and a Slater determinant

This may belong in Chemistry, but I thought I might try my luck here first. In Szabo's book, an exercise requires a proof that = (N!)^(1/2) * given that |K(HP)> is the Hartree product wave ...
4
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2answers
101 views

Where does the electron get its high magnetic moment from?

I have always found the concept of spin a little weird. I had read somewhere that for the charge or size of electrons, their magnetic field is very high. In order to produce such fields, they must be ...
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1answer
41 views

Adding versus multiplying identical photons' wavefunctions?

I am currently confused with understanding many identical photons' wavefunctions. I think that photon wavefunctions are supposed to be multiplied together to describe the total state of all bosons. ...
4
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1answer
145 views

Noether's Theorem: Foundations

I'm wondering on what principles Noether's theorem foots. More precisely: The action is a functional on the fields only. Why do we consider then variations of the space time too? In principle careful ...
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0answers
34 views

Writing Schrodinger equation with central potential in Atomic unit

I'm struggling to write Schrodinger equation with a central potential in Atomic unit. $$ ...
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0answers
44 views

What is the transpose of the displacement operator? [closed]

How do we calculate the transpose of this expression? $$ \hat{D}(\alpha) = \exp \left( \alpha \hat{a}^\dagger - \alpha^* \hat{a}\right) $$ What is the simplified result? Displacement Operators: ...
4
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3answers
119 views

When you measure position of an electron in a energy pure state, what happens to the energy?

When you measure the position of an electron that is in a pure energy state, what happens the energy becomes non-deterministic. That is future measurements of energy can only be predicted with respect ...
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1answer
49 views

Can an electron spontaneously be emitted/ejected from a hydrogen atom?

In elementary QM, an electron is typically viewed as a cloud around a proton. The idea is that it's position can only be determined once a measurement is made. The probability that the electron will ...
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1answer
58 views

Is this double “double slit experiment” involving entanglement possible?

The experiment goes as follows: Put a particle emitter (photon, electron etc.) between a pair of double slits. The emitter launches pairs of particles that are entangled in such a way that if one ...
2
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1answer
67 views

Is this theory about Universe information true?

I recently saw this video about information and randomness. At some point, it states that a completely predictable universe would infringe the second law of thermodynamics, because it would imply that ...