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 quantum-field-...

learn more… | top users | synonyms (4)

3
votes
1answer
86 views

Is there any Hamiltonian that contains time derivative? [duplicate]

Quantum mechanics is governed by Schrodinger's equation: $$\hat{H}\psi=i\hbar\partial_t \psi$$ It seems that Hamiltonian acts on wave functions like a time derivative. Just out of curiosity, is ...
3
votes
1answer
117 views

Replacing fermionic operators with their Fourier transform and boundary conditions

In the section 4.1 of Quantum Computation by Adiabatic Evolution, Farhi et al proposes a quantum adiabatic algorithm to solve the $2$-SAT problem on a ring. To compute the complexity of the algorithm ...
6
votes
4answers
780 views

If an isolated quantum system consists of only one particle, is it possible for it to be in a mixed state?

Mixed states are defined as the statistical ensemble of pure states. Classically, I understand the word, "statistical" referring to a system with a large number of microscopic particles. So if I go ...
3
votes
2answers
78 views

Meaning of non-degenerate photon pair

I am seeing in a lot of papers about quantum optics the term "non-degenerate photon pair", which seems like a very important concept. This may seem like a silly question, but I am an EE undergrad who ...
2
votes
0answers
84 views

Some questions about the Kitaev Chain Model

In the paper,'Unpaired Majorana Fermions in Quantum Wires', Kitaev shows that unpaired Majorana Modes can be found at the end of a Quantum Wire for certain conditions. The effective Hamiltonian ...
-4
votes
0answers
32 views

Is there an explanation to Heisenberg's Uncertainty principle? [duplicate]

I watched a video witnessing Heisenberg's Uncertainty principle in action. I'm wondering is there an "explanation" (not on basis of observations) to it? p.s. Consider me a noob before answering.
0
votes
2answers
102 views

Total spin of system of two spin-$1/2$ particles

Consider a quantum system of two spin one half particles. Let $\alpha(1)$ be 'spin up' for first system, and $\beta(1)$ 'spin down' for first system, and likewise for second system. We have $$ \chi = \...
3
votes
1answer
53 views

Is it possible to create a pair of polarized, polarization-entangled photons?

Is there a light source which emits (mostly) polarization-entangled pairs of photons that have a known polarization angle, e.g. a certain angle in relation to the orientation of the source? Applying ...
3
votes
1answer
62 views

Tensor product representation of $SO(3)$ in the Hilbert space of particle with spin $S$

For a particle with a spin $S$, the rotation operator is given by $$ e^{iJ_i\theta/\hbar} $$ where $J_i$ is the component of the total angular momentum along the direction of the rotation axis. The ...
3
votes
2answers
91 views

What kets represent on QFT?

In Quantum Mechanics kets are used to represent states of a system. This is indeed well written in the first postulate of Quantum Mechanics which states that to describe a quantum system we use a ...
3
votes
1answer
42 views

Aim of photon gun in a double-slit experiment

Hope someone can enlighten me on the following questions: In a double-slit experiment with photon, how is the photon gun aimed? If the photon gun is set up to aim at the barrier space between the ...
4
votes
2answers
106 views

Do quantum leaps happen in random directions?

Regarding quantum "leaps" or "jumps" (also known as atomic electron transition) -- do these leaps happen in what would appear to be random directions, or do they happen according to some rule, such as ...
0
votes
0answers
21 views

cause of brownian motion's indeterminacy

Is there a causal link between quantum property indeterminacy (randomness) and a complex molecule's location in space in any moment at larger scales aka brownian motion? This question is void if my ...
0
votes
1answer
71 views

Common basis for angular momentum and Hamiltonian, harmonic oscillator

Suppose a two dimensional isotropic harmonic oscillator. We define the angular momentum operator as $L = XP_y - YP_x$, where $X,Y$ are the position operators and $P_x,P_y$ are the momentum operators. ...
0
votes
1answer
48 views

Applying controlled Hadamard gate

I am unable to explain the output of a controlled Hadamard gate. If U is a single qubit gate U= $\begin{pmatrix}u11 & u12\\ u21 & u22\end{pmatrix}$ then the controlled gate is controlled U ...
1
vote
0answers
47 views

How can we justify identifying the Dirac delta function with the eigenfunction of position? [duplicate]

I can think of at least two different ways to understand eigenfunctions of operators in quantum mechanics. But neither one seems to provide a good explanation for why we take the position-basis ...
2
votes
0answers
38 views

Bound states in two and three dimensional delta potential in non relativistic QM

I would like to find bound state energies in let's say 2D delta function potential. So my eigenvalue equation is: $$(-\frac{1}{2}\Delta - g\delta(r)) \psi = -B \psi$$ and by the means of Fourier ...
1
vote
1answer
109 views

Functional Analysis for Quantum Mechnanics [duplicate]

I have completed three sequences of courses in QM, and I'm very much eager to to do the functional analysis of QM on my own in my spare time. Can someone suggest some books? I like books with ...
1
vote
1answer
61 views

Solution for Schrödinger equation for constant box potential?

It is known that in a box potential, when we set $V = 0$ inside and $V = \infty$ on the boundaries, the solution to the equation $$ - \frac{\hbar}{2m} \bigg( \frac{\partial^2}{\partial x^2} + \frac{ \...
0
votes
2answers
79 views

How can I show that $\mathrm{Tr}\left( f(G^\dagger G)\right)=\mathrm{Tr}\left( f(G G^\dagger)\right)$?

I'm slightly stuck on the following question: Prove that: $\mathrm{Tr}\left( f(G^\dagger G)\right)=\mathrm{Tr}\left( f(G G^\dagger)\right)$ where $G$ is any operator. Using the definition of the ...
3
votes
3answers
137 views

Hilbert Space axiom in QM

My question is about the standard axiom on Hilbert's space in orthodoxal QM. It seems that this axiom appeares actually as an external pure mathematical axiom in all textbooks. Say, Mackey introduces ...
2
votes
1answer
68 views

Are the 'clock' and 'shift' operators used in Qudit codes physically realizable?

I've recently started doing some reading on the subject of qudit codes. In particular, i'm interested in the frequently used clock and shift operators. Can these operators be physically realized? Or,...
3
votes
1answer
45 views

Emissions of radioactive particles travelling near the speed of light vs stationary particles

Sorry in advance if this is a noob question. I just heard another explanation of special relativity and was wondering about it. If a radioactive particle was passing by near the speed of light, would ...
2
votes
1answer
97 views

Calculating the boundary modes in Kitaev Chain

In section 2 of the paper, 'Unpaired Majorana Fermions in Quantum Wires', equation (14), the following transformation: \begin{equation} b^{'} = \sum_{j} (\alpha_+ ^{'} x_+ ^{j} + \alpha_- ^{'} x_- ^{...
0
votes
0answers
32 views

How to understand Superconductivity in a particle number fixed system at zero temperature?

The BCS wave function doesn't have fixed particle number. And this is called U(1) symmetry breaking by many people. But if we are given a system with fixed particle number, how can we understand ...
0
votes
0answers
59 views

Confused about the substitution of the fermionic operators with their Fourier transform in an adiabatic Hamiltonian

In the section 4.1 of Quantum Computation by Adiabatic Evolution, Farhi et al proposes a quantum adiabatic algorithm to solve the $2$-SAT problem on a ring. To compute the complexity of the algorithm ...
0
votes
1answer
45 views

Compton wavelength And universe expansion

I'd like to ask stupid question. As I understand the wavelength of photons increase in time due to universe expansion. And it seems that Compton wavelength of particles does not changes in the same ...
1
vote
0answers
63 views

Stark effect in Polonium and Plutonium

I found the following question given as an exercise in one lecture notes: What are differences between Stark effect in Polonium and Plutonium ? What are differences between Stark effect in light ...
4
votes
2answers
132 views

Occupation of quantum states at room temperature

I'm reading up on the physics of degenerate matter (in "An Introduction to Modern Astrophysics" by Carroll & Ostlie, section 16.3), and the impact of electron degeneracy pressure. I came across ...
3
votes
2answers
127 views

Quantum non-unitary transformation? [closed]

Let us say that I apply a non-unitary transformation $\def\ket#1{| #1\rangle} \def\braket#1#2{\langle #1|#2\rangle} \hat A$ to the ket's: $$\ket{\psi} \rightarrow \hat A \ket{\psi}$$ $$\ket{\phi}\...
3
votes
1answer
134 views

Is it possible to build a logical theory in QM based on quantum logic? [closed]

Quantum Probabilities as Bayesian Probability, Quantum probabilities as degrees of belief Above are two articles about quantum Bayesianism. I don't know why quantum Bayesianism use some results from ...
1
vote
1answer
36 views

Dirac notation - trace of product of (bipartite) density matrices

I'm getting confused by the Dirac notation. Suppose I have the following two objects. $$\rho = \sum_k p_k (\rho_A \otimes \rho_B) = \sum_k p_k |k \rangle \langle k | \otimes |k\rangle \langle k | ,$$...
2
votes
1answer
45 views

How to measure relative phases of quantum states

If I have a large number of identical systems in identical quantum state $\Psi$ and an observable $A$ whose eigenstates are $\alpha_n$: $$ \Psi = \sum_n c_n \alpha_n $$ I can get absolute values ...
4
votes
4answers
587 views

Are quantum operators dimensionless?

I'm slightly confused as to whether quantum (hermitian) operators, which we get by promoting observables to operators, are dimensionless or not? Clearly the Hamiltonian of the system, say of the ...
0
votes
0answers
53 views

Why is there a state which is annihilated by two different operators with same absolute Fourier index?

In the section 4.1 of Quantum Computation by Adiabatic Evolution, Farhi et al proposed a quantum adiabatic algorithm to solve the $2$-SAT problem on a ring. To compute the complexity of the algorithm ...
0
votes
1answer
33 views

Reasoning behind taking the Fourier transform of the fermionic operators for a circular $1$D spin chain [closed]

In the section 4.1 of Quantum Computation by Adiabatic Evolution, Farhi et al proposes a quantum adiabatic algorithm to solve the $2$-SAT problem on a ring. To compute the complexity of the algorithm ...
0
votes
1answer
28 views

Boundary value condition used during Jordan-Wigner transformation for a $1 D$ Ising chain

In the section 4.1 of Quantum Computation by Adiabatic Evolution, Farhi et al proposes a quantum adiabatic algorithm to solve the $2$-SAT problem on a ring. To compute the complexity of the algorithm ...
0
votes
0answers
26 views

Time reversal symmetry and vanishing matrix element

In the lecture today we went through the following example: Time-reversal symmetry requires that the matrix element $M_i=\langle \psi_i|z|\psi_i\rangle$ vanishes if the state has definite $|j\;m\...
1
vote
1answer
48 views

Reason behind choosing the invariant states for an operator which commutes with an adiabatic Hamiltonian

In the section 4.1 of Quantum Computation by Adiabatic Evolution, Farhi et al proposes a quantum adiabatic algorithm to solve the $2$-SAT problem on a ring. To compute the complexity of the algorithm ...
0
votes
1answer
50 views

Direction of momentum given by the de Broglie relation

The momentum of an electron can be computed by the well-known classical mechanics equation: $p=mv$ where $m$ is the mass of an electron, and $v$ is its velocity. In this case, since $v$ is a vector,...
-1
votes
0answers
37 views

what is the plane of the matter waves?

We all know that in an electromagnetic waves there is one wave whose plane is perpendicular to the other. so you see that there is a plane and every book which i have read shows the same. now i come ...
1
vote
3answers
97 views

What is meant by rest in rest-mass?

As far as I know only photons are considered to have no rest-mass. In common words when it doesn't move it 'disappears'. Electrons and quarks should have a rest-mass. But are they really at rest? ...
0
votes
1answer
60 views

Does the Hamiltonian time-evolution operator actually change the state of the system?

According to my understanding of things, the time evolution operator in QM looks something like this, $$U = \exp(-iHt/\hbar)$$ Which acts on the state vector / wave-function of the system to ...
0
votes
2answers
57 views

What kind of product is $\prod^n_{j=1}\sigma^{(j)}_x$?

In the section 4.1 of Quantum Computation by Adiabatic Evolution, Farhi et al proposes a quantum adiabatic algorithm to solve the $2$-SAT problem on a ring. The adiabatic Hamiltonian is defined as $$...
1
vote
2answers
88 views

Measurement in many body systems

Any wavefunction for a system of many particles can be decomposed into linear combinations of the direct product of single particle states with respect to a certain observable(single particle basis). ...