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)

4
votes
2answers
109 views

Independent systems and Lagrangians

Definition 1: The notion of independent systems has a precise meaning in probabilities. It states that the (joint) probability or finding the system ($S_1S_2$) in the configuration ($C_1C_2$) is ...
4
votes
2answers
574 views

Proof for commutator relation $[\hat{H},\hat{a}] = - \hbar \omega \hat{a}$

I know how to derive below equations found on wikipedia and have done it myselt too: \begin{align} \hat{H} &= \hbar \omega \left(\hat{a}^\dagger\hat{a} + \frac{1}{2}\right)\\ \hat{H} &= ...
2
votes
1answer
4k views

Where is the amplitude of electromagnetic waves in the equation of energy of e/m waves? [duplicate]

Does the amplitude of the photon oscillations always stay constant and if it is not - what are the physical differences between the photon with higher amplitude in comparison to the one with the less ...
4
votes
3answers
249 views

Reaching the speed of light via quantum mechanical uncertainty?

Suppose you accelerate a body to very near the speed of light $c$ where $v = c - \epsilon$. Although this would take an enormous energy, is it possible the last arbitrarily small velocity needed -- ...
5
votes
2answers
430 views

Do we always ignore zero energy solutions to the (one dimensional) Schrödinger equation?

When we solve the Schrödinger equation on an infinite domain with a given potential $U$, much of the time the lowest possible energy for a solution corresponds to a non-zero energy. For example, for ...
3
votes
1answer
226 views

Difference between vector and pseudo-scalar

In physics, a pseudo-scalar is a quantity that behaves like a scalar, except that it changes sign under a parity inversion such as improper rotations while a true scalar does not. Can someone show me ...
3
votes
1answer
226 views

The matrix element of a normal-ordered operator

Eq (1.137) in Negele and Orland gives the following identity for a normal-ordered operator $A(a_i^\dagger,a_i)$: $$\langle \phi|A(a_i^\dagger,a_i)|\phi'\rangle=A(\phi_i^*,\phi'_i)e^{\sum ...
5
votes
2answers
631 views

In quantum mechanics(QM), can we define a high-dimensional “spin” angular momentum other than the ordinary 3D one?

Inspired by my previous question Questions about angular momentum and 3-dimensional(3D) space? and another relevant question How to define angular momentum in other than three dimensions? , now I get ...
-1
votes
1answer
125 views

EM Waves Energy Loss

Where does the energy go when two photons interfere destructively at a point on a screen in Young's double slit experiment ?
2
votes
2answers
673 views

Hamiltonian of Harmonic Oscillator with Spin Term

We have the usual Hamiltonian for the 1D Harmonic Oscillator: $\hat{H_{0}}=\frac{\hat{P^2}}{2m} + \frac{1}{2}m \omega \hat{X^2}$ Now a new term has been added to the Hamiltonian, $\hat{H} = ...
11
votes
1answer
968 views

What're the relations and differences between slave-fermion and slave-boson formalism?

As we know, in condensed matter theory, especially in dealing with strongly correlated systems, physicists have constructed various "peculiar" slave-fermion and slave-boson theories. For example, For ...
3
votes
0answers
515 views

projective measurement & POVM

Let us consider the following completely positive map $\mathcal{B}(\mathbb{C}^n)\ni\rho\mapsto L\rho L^\dagger$, where $L\in\mathcal{B}(\mathbb{C}^n)$ is any arbitrary operator (and can have rank ...
2
votes
1answer
163 views

Physical significance of effective wave function

In Yanhua Shih's book on quantum optics, the coherence functions are expressed in terms of effective wave function. Here are the expressions for single photon wave packets. To derive the coherence ...
5
votes
2answers
294 views

Integer physics

Are there interesting (aspects of) problems in modern physics that can be expressed solely in terms of integer numbers? Bonus points for quantum mechanics.
2
votes
1answer
953 views

Dark and bright areas around atoms in a scanning tunnelling microscope image

Recently IBM created world’s smallest ever animation on an atomic scale video. Researchers made the animation using a scanning tunnelling microscope to move thousands of carbon monoxide molecules to ...
8
votes
3answers
1k views

Determinism, classical probabilities, and/or quantum mechanics?

[I]f you want a universe with certain very generic properties, you seem forced to one of three choices: (1) determinism, (2) classical probabilities, or (3) quantum mechanics. [My emphasis.] ...
6
votes
0answers
143 views

$U(N)$ gauged quantum mechanics

I'm studying the $U(N)$ gauge theory theory in 0+1 dimensions. The aim is to show that this is equivalent to a matrix model. Is there any literature on this topic? The action I am interested in is ...
2
votes
0answers
59 views

Standard Quantum Mechanics representation as a constrained 2 + 1 space-time (membrane) theory?

Could a particular Standard Quantum Mechanics representation be a constrained 2 + 1 space-time theory (membrane theory) ? (i) This question is motivated by a possible (approximative) analogy with ...
2
votes
2answers
146 views

Qubit projections

Given the qubit: $$\frac{|0\rangle+i|1\rangle}{\sqrt{2}}$$ What is the corresponding point on the extended complex plane and Bloch sphere? How to perform calculations and get the point representing ...
0
votes
1answer
363 views

Time Dependent HydroHow would I go about writing the time dependent wave function given the wavefunction at $t=0$? gen Wave Function

1) How vwoulHow would I go about writing the time dependent wave function given the wavefunction at $t=0$? go about writing the time dependent wave function given the wavefunction at $t=0$? ...
3
votes
2answers
378 views

QM formalism is one big confusion - lack of geometrical explaination with images

I have been trying to learn QM and it went well (all untill harmonic oscilator) until i had to face the formalism: Hilbert space- As a novice to QM i am very sad that in none of the books i have ...
3
votes
3answers
906 views

How do I determine the location of a free particle with Schrödinger's equation?

I'm trying to get to grips with the Schrödinger equation by looking at a free particle. I'm certain at some point I massively misunderstood something. According to a textbook and a lecture the free ...
5
votes
2answers
2k views

Translator Operator

In Modern Quantum Mechanics by Sakurai, at page 46 while deriving commutator of translator operator with position operator, he uses $$\left| x+dx\right\rangle \simeq \left| x \right\rangle.$$ But for ...
4
votes
1answer
357 views

Moyal Product in Non Commutative Quantum Mechanics

Can someone please explain me what is a Moyal product? Also, how does putting $$X_a(\psi) ~=~ x_a\star\psi$$ realise $$[X_a,X_b]=i\theta_{ab}{\bf 1}?$$ Ref: Quantum mechanics on non-commutative ...
3
votes
2answers
138 views

Why does the quantum eraser seem to violate energy and momentum conservation?

In the literature of the quantum eraser experiment it is argued that the change in statistics of the system from non-interference to interference is due to the erasing of "distinguishing information". ...
1
vote
1answer
728 views

Mathematical explanation of quantum teleportation

I am now studying quantum teleportation. I get what the process is like but I'm wondering why it happens this way. You've got two entangled particles A and B whose wavefunctions are entangled. You ...
1
vote
0answers
89 views

What is the difference between Cramer and Vaidman?

Two very interesting new papers on arXiv last night by Lev Vaidman and friends lead me to ask about the differences between Cramer's transactional interpretation of quantum mechanics (TIQM) and the ...
5
votes
1answer
370 views

Can a photon exhibit multiple frequencies?

Can a photon be a superposition of multiple frequency states? Kind of similar to how an electron can be a superposition of multiple spin states.
2
votes
4answers
2k views

How is the hamiltonian a hermitian operator?

My book about quantum mechanics states that the hamiltonian, defined as $H=i\hbar\frac{\partial}{\partial t}$ is a hermitian operator. But i don't really see how I have to interpret this. First of ...
0
votes
0answers
82 views

What does this notation mean in terms of quantic numbers, and how to imagine the electrons in this quantic system? (Helium $2^1$ $P$ and $2^3$ $P$)

Helium atom in the $2^1$ $P$ and $2^3$ $P$ excited states Now I'm guessing that 1 electron should be considered in the 1s state, but what about the other? Should I consider the other as simply ...
-1
votes
1answer
71 views

Heisenberg's uncertainty and $0 K$ temperature

when a body is subjected to $0 K$ temperature, it becomes rigid. hence if we see in terms of quantum the lattice vibration decreases, resulting in no change in the direction of the Random velocity, ...
3
votes
1answer
685 views

Schrödinger equation for a harmonic oscillator

I have came across this equation for quantum harmonic oscillator $$ W \psi = - \frac{\hbar^2}{2m}\frac{d^2\psi}{dx^2} + \frac{1}{2} m \omega^2 x^2 \psi $$ which is often remodelled by defining a new ...
0
votes
1answer
123 views

What is inner product of the vacuum state with itself?

If $|0 \rangle$ is the vacuum state in quantum mechanics and $\alpha$ is any complex number, what is $\langle 0 | \alpha | 0 \rangle$? I need to have that $\langle 0 | \alpha | 0 \rangle = \alpha$, ...
2
votes
1answer
524 views

Matrix representation for fermionic annihilation operator

My guess it should look something like this: $ c_\sigma = ...
3
votes
0answers
133 views

Laughlin state unique ground state?

In the FQHE, one typically encounters the statement that the $\nu = 1/3$ Laughlin state is a unique exact ground state of a model Hamiltonian where the Haldane pseudopotentials $V_1 \neq 0$ and $V_m = ...
2
votes
0answers
48 views

Quantum harmonic oscilator - book that does it all right [duplicate]

I am dealing with quantum harmonic oscillator. In every single book or video i have checked out i can read how the mathematical technique for solving this Schrödinger equation: $$ W\psi = - ...
2
votes
1answer
150 views

Is Dirac's description of a photon in a split beam still seen as correct today?

This comes from the Interference of Photons section in the book The Principles of Quantum Mechanics by P Dirac: We shall discuss the description which quantum mechanics provides of the ...
8
votes
2answers
5k views

De Broglie wavelength, frequency and velocity - interpretation

Two fundamental equations regarding wave-particle duality are: $$ \lambda = \frac{h}{p}, \\ \nu = E/h .$$ We talk about de Broglie wavelength, is it meaningful to talk about de Broglie frequency ...
3
votes
0answers
68 views

Perturbation in Supersymmetric Quantum Mechanics.

To do perturbation analysis of Supersymmetric Quantum Mechanical Hamiltonian, the superpotential is first scaled by a constant $\lambda >> 1$ and then expanded about it's critical point. Finally ...
1
vote
2answers
279 views

Purpose of Grover's algorithm?

How is the output of Grover's algorithm useful if the result is required to use the oracle? If we already know the desired state, what's the point of using the algorithm? So can you give me a ...
0
votes
2answers
710 views

Quantum tunneling is faster than light travel?

Quantum tunneling is faster than light travel ? My reasoning is that the particle cannot be detected inside the tunnel so if it travels from A to B it must be instantly going from A to B , hence ...
3
votes
1answer
241 views

Discretization of action in path integral

I am reading Peskin and Schroeder (path integrals) and it states that discretising the classical action gives: $$S~=~\int \left(\frac{m}{2}\dot{x}^{2}-V(x)\right) dt ~\rightarrow~ \sum ...
1
vote
0answers
83 views

Hamiltonian matrix propertu

A professor made an statement to prove the variational theorem: Because the Hamiltonian (H operator of quantum physics) is diagonal in its own eigenfunction, the terms in $\left \langle \Phi _{m} ...
0
votes
1answer
58 views

Violation of the Normalization Constraint?

Say we have two qubits $|a\rangle$ and $|b\rangle$ both initialized to $|0\rangle$. We then apply the rotation gate $R_{x}(\frac{\pi}{2})$ of matrix representation $\left( \begin{array}{} ...
4
votes
1answer
537 views

Questions about angular momentum and 3-dimensional(3D) space?

Q1: As we know, in classical mechanics(CM), according to Noether's theorem, there is always one conserved quantity corresponding to one particular symmetry. Now consider a classical system in a $n$ ...
3
votes
2answers
498 views

Quantum commutator

I'm given this commutator: $$\left[PXP,P\right]$$ Being $P\psi=-i\hbar\partial_x\psi$, and $X\psi=x\psi$ I've solved it in two ways, the first one is just aplying the commutator to some function ...
0
votes
1answer
273 views

is really an atom stable?

Half filled and fulfilled atomic orbitals are stable because of : high exchange energy. The problem is with exchange energy. We have learnt that the half and fulfilled orbitals have maximum no. of ...
2
votes
3answers
1k views

Can an electron interact with itself to create interference?

I have been recently brushing up my elementary physics concepts, specifically quantum physics. So, if I set up a single photon emitter in the double slit experiment, it is possible for me to see ...
1
vote
1answer
44 views

Name of a state with $d-1$ excitations, distributed uniformly among $n$ qudits

Is there a particular name for a quantum state of the form (up to the normalization): $$\sum_{i_1+\ldots+i_n = d-1} |i_1\rangle |i_2\rangle \ldots |i_n\rangle$$ or was it studied is some papers? ...
1
vote
1answer
1k views

Hermitian Adjoint of differential operator

I came across this equation (identity) (Eq. 4 in this paper): $\int(-i d\psi/dx)^*\psi dx = \int \psi^*(-i d\psi/dx) dx + id(\psi^*\psi)/dx\mid_{-\infty}^{+\infty}$ I have trouble proving it. I ...