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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2answers
32 views

If outside a cylindrical solenoid exist an electrical field what does that mean to the Aharonov-Bohm Effect?

To the question "What is the electric field outside a cylindrical solenoid when inside is turned on a magnetic field" the answer is that outside exists a electric field. Does that mean that the ...
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0answers
22 views

What is the most general definition of a bosonic Gaussian state?

I am reading this paper where the definition of the bosonic state is mentioned on page 2 here :- http://arxiv.org/pdf/0806.1625.pdf . From a general definition of any density operator in terms of ...
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3answers
65 views

Can stimulated emitted photons be absorbed?

Typically a stimulated photon will be one of a pair with its stimulating photon. If the leading photon is absorbed by a particle in the ground state, will it then be re-emited by the stimulated ...
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5answers
206 views

About the definition of expectation value in quantum mechanics

In quantum mechanics, the expectation value of a observable $A$ is defined as $$\int\Psi^*\hat A\Psi$$ But in probability theory the expectation is a property of a random variable, with respect to a ...
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1answer
62 views

Showing Dirac equation's Lorentz invariance and use of unitary matrix $U$

Dirac equation is $i \hbar \gamma^\mu \partial_\mu \psi - m c \psi = 0 $ To show its Lorentz invariance, we convert spacetime into $x'$ and $t'$ from $x$ and $t$ and then $( iU^\dagger \gamma^\mu ...
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1answer
92 views

Quantum states and state vectors

Does a state vector correspond to only one quantum states and the components in the state vector correspond to different states of this quantum state or is it that the components of the state vector ...
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2answers
89 views

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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0answers
20 views

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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1answer
74 views

How to compute observables from the boson field operator?

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
78 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
38 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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0answers
28 views

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

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
68 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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2answers
80 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 ...
3
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0answers
37 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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0answers
50 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
37 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
46 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
69 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 ...
3
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2answers
104 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 $$ U(x_b,x_a;T) = \langle x_b | U(T) |x_a \rangle= \int \mathcal{D}q e^{iS} \tag{1} $$ ...
2
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2answers
99 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 ...
0
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1answer
33 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
49 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
138 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
61 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
82 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 ...
2
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1answer
50 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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0answers
68 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 ...
3
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1answer
94 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) . ...
3
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4answers
442 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 ...
3
votes
1answer
90 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 ...
3
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1answer
87 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 ...
2
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0answers
48 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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1answer
73 views

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

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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0answers
35 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
66 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
84 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 ...
3
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0answers
53 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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0answers
46 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 ...
0
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1answer
56 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 ...
1
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1answer
110 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
87 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 $E/c^2$, ...
2
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4answers
150 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
304 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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0answers
20 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
votes
2answers
121 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
42 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
147 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
35 views

Writing Schrodinger equation with central potential in Atomic unit

I'm struggling to write Schrodinger equation with a central potential in Atomic unit. $$ ...
4
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3answers
121 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 ...