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-...

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1answer
57 views

Doesn't quantum uncertainty disprove string theory? [duplicate]

String theory states that the oscillations of little strings are responsible for all the particles in and the evolution of the universe. The specific type of particle created by a string depends on ...
0
votes
1answer
25 views

Corrections to the Bohr energies of Hydrogen [on hold]

Among fine structure, Hyperfine splitting and Lamb shift, why Hyperfine splitting is the smallest while Fine structure is the largest?
1
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1answer
50 views

What happens to the visible light that a substance does not reflect on an atomic level?

Let's say we have a blue, opaque material. If white light was incident on that material, the blue light would be absorbed by electrons and the electrons would transition to a higher energy state, and ...
2
votes
0answers
28 views

Degeneracy of energy levels of a particle in a spherical step potential?

I have a particle of mass $m$ and spin $1/2$, in a spherical step potential, $$ V(r) = \begin{cases} 0 & r<a, \\ V_0 & r>a. \end{cases} $$ Now they ask me to find, without solving the ...
0
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0answers
51 views

Entanglement of bi- and tripartite pure and mixed states

since I'm not sure on how to find out whether a system is entangled or not I thought about examples that could clarify the whole thing. first example: system is in the state $\rho=1/2 (| 000 \rangle \...
-1
votes
2answers
70 views

Why don't electrons moving around in a orbit produce electromagnetic waves in their natural state? [duplicate]

If moving electrons produce changing electric field, and if changing electric field produces magnetic field, every electron must produce an electromagnetic wave. This means an atom in its natural ...
0
votes
2answers
69 views

Completeness relation for coherent states of the quantum harmonic oscillator

For the Quantum harmonic oscillator with energy eigenstates $|n\rangle$ one defines a coherent state for every complex number $z$ by setting (note that the normalization varies across the literature) $...
2
votes
3answers
87 views

Bell inequality violations evidence for 1935 EPR claims?

Is it possible that Bell inequality tests provide experimental evidence in support for the EPR claims in their 1935 paper titled "Can Quantum-Mechanical Description of Physical Reality Be Considered ...
-5
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0answers
43 views

Why is the Heisenberg uncertainty priciple considered as a universal truth? [duplicate]

You should have heard about Heisenberg and his uncertainty principle. I want to know why it is considered as a universal truth, and not a technological limitation. I'd prefer an elaborate answer with ...
1
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1answer
55 views

Trouble understanding Nielsen & Chuang exercise

I am probably just stuck on something very simple, but I'm having trouble understanding a premise of Exercise 10.40 in Nielsen & Chuang. The full details of the exercise are not important for my ...
3
votes
1answer
73 views

Problem with figuring out sign conventions in QFT

I have a problem with sign conventions in QFT which I have trouble dealing with myself. I self-study and mainly use Weinberg and Peskin. I will present the reasoning following conventions adapted by ...
1
vote
1answer
56 views

Using the momentum-space definition of the position operator in position space?

For the position operator $\hat X$: $\hat X \rightarrow x$ in position space $\hat X \rightarrow i \frac{\partial}{\partial k_x}$ in momentum space Question: Can $\hat X \rightarrow i \frac{\...
1
vote
1answer
79 views

Why don't the internal electric and nuclear forces holding atoms and molecules together cause decoherence during a buckyball double-slit experiment? [on hold]

My understanding is that anything that qualifies as an "observation" or "measurement" will cause the "fuzziness" of the superposition to disappear to the local observer, and the results of said ...
4
votes
3answers
293 views

Dummy variables in Dyson series

In the Dyson series, it is known that: \begin{align} {\cal T}\exp\left[-\frac{i}{\hbar}\int_0^tH(t')dt'\right] &= I - \frac{i}{\hbar} \int_{0}^{t} dt' H(t') + \left(-\frac{i}{\hbar}\right)^2 \...
3
votes
1answer
64 views

Integral form of solution of Dyson series and differentiation of the exponential form

The solution to time dependent hamiltonian equation is: $$\frac{\partial}{\partial t}U(t) = -\frac{i}{\hbar}H(t)U(t)$$ The immediate integral form solution is $U(t) = I - \frac{i}{\hbar}\int_{0}^{...
-1
votes
0answers
23 views

Probability of expectation value of energy wave function at initial time [closed]

If a quantum harmonic oscillator wave function with energies $$E_n = (n+1/2)\hbar\omega$$ is given by $$\Psi(x,0)=\frac{1}{\sqrt{10}}\left[3\phi_0(x)+\phi_1(x)\right]$$ where $\phi_0(x)=\left(\frac{m\...
-2
votes
0answers
24 views

Which linear transformations are more abundant: dimension-increasing, preserving or decreasing? [migrated]

My final aim is to understand the increase of Von Neumann Entropy in quantum systems by analyzing classes of unitary matrices in finite-dimensional Hilbert spaces. I'm following a potentially very ...
0
votes
1answer
56 views

Does a Polarizing Beam Splitter Cause Wave Function Collapse?

For a single photon, its polarization can be a superposition of two orthogonal bases (e.g. horizontal or vertical). However, as I understand, once it has been measured, it must collapse into one of ...
0
votes
0answers
33 views

Does the unboundedness of the potential mean necessarily there is no normalizable state? [closed]

Consider the Hamiltonian $ H = p^2 + V(x)$. Suppose the potential $V$ is unbounded from below in at least one direction ($x \rightarrow \pm \infty $). Does this necessarily mean that there exists no ...
-2
votes
0answers
42 views

Problems on rectangular well [closed]

We have a rectangular potential well from $x=-b$ to $x=a$.Can we divide the well into two parts from $x=-b$ to $0$ and $x=0$ to $a$ to solve Schrodinger equation?Actually,I want to know how to solve ...
1
vote
0answers
47 views

Normalizable eigenvectors of the inverted harmonic oscillator

Consider the inverted harmonic potential $V(x) = - x^2 $. Does the corresponding Hamiltonian $$ H = p^2 - x^2 $$ have any normalizable eigenstate? How about $$ H = p^2 - x^4 ? $$ Any good ...
0
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0answers
36 views

Systems with extensive ground state degeneracy

This is sort of a follow up to this question: What does it mean for a Hamiltonian or system to be gapped or gapless? There it is stated in one of the answers that a system is gapped if it fulfills ...
1
vote
1answer
68 views

De Broglie wave length of electron [closed]

Consider an electron with total energy $E>V_2$ in a potential well with $$V(x)= \begin{cases} \infty & x< 0 \\ V_1 & 0< x< L \\ V_2 & x>L \end{cases} ...
1
vote
1answer
83 views

When is a quantum state stationary?

If a quantum state is an eigenstate of the Hamiltonian, then it is stationary. But can a state be stationary if it is not an eigenstate of the Hamiltonian? If yes, how can one prove whether a state is ...
0
votes
3answers
68 views

What is the Meaning of the Superposition Principle

I am a bit confused as to what the superposition principle actually means. Does it merely mean that you can express any given state as the linear combination of two vectors? If so, isn't that kind of ...
0
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0answers
28 views

Measured Polarization for a Single Photon

I understand that for a given beam of light, it can exist in any number of polarizations. However, I have been told that given a single photon, it can only exist as horizontally or vertically ...
1
vote
3answers
79 views

Transforming Qubits Into Bits

From what I understand, a qubit exists in a superposition of states and once it has been measured, it must fall into one of the two possible states. Now, I have been told that once a qubit is measured,...
0
votes
1answer
34 views

Representation of spin operators in a two electrons system

I've studied that the spin space of an electron is a two-dimensions Hilbert space. A possible representation of this space can be constructed defining: $$\chi_+ = \begin{pmatrix}1 \\ 0 \end{pmatrix} \...
1
vote
0answers
41 views

Atom-photon interaction

When we describe interaction of atom with EM field, we consider the interaction term in Hamiltonian as follows $$ W(t) = -\frac{e}{2\mu c} (\hat{A} \hat{p} + \hat{p} \hat{A}) + \frac{e^2}{2\mu c^2} \...
0
votes
2answers
43 views

Calculating the product state capacity of the quantum depolarizing channel

This is homework, so just let me know if I'm on the right track or where I went wrong, please. So, we are asked to compute the product state capacity $$C_1(T) = \max_{\{p_j,\,\vert \psi_j\rangle\}}\...
2
votes
2answers
54 views

Quantum Logic Gates

In classical computation, a bit can have the value of either 1 or 0 and one can apply a logic gate to this bit. As far as I understand, in classical computation, no matter what gate is used, the value ...
2
votes
2answers
49 views

Born's interpretation for momentum operator

Hi I have a basic QM question: Given a state vector $|\psi(t) \rangle$, at some time $t$, we can project this onto the position basis, $\langle \vec{r}| \psi(t) \rangle = \psi(\vec{r},t)$. Then from ...
0
votes
1answer
18 views

Inverting squeezing and displacement operators

This question is about inverting the product of squeezing operator and a displacement operator in the following way: I have $D(\alpha)S(\xi)$ and I'd like to turn it into $S(\xi')D(\alpha')$. Where $...
1
vote
0answers
16 views

Elimination of extra phases in adiabatic formula

Can someone explain to me how the additional phase factor $\gamma_n(t)$ in the adiabatic formula can be eliminated (not just mentioning gauge transformation, but showing why $\gamma_{n}(t)$ can but $\...
1
vote
1answer
56 views

$\frac{1}{\sqrt{2}}(1 + i)|0\rangle$ on the Bloch sphere

By definition, a quantum state can be expressed as $$|\psi\rangle = a |0\rangle+b |1\rangle.$$ Here, $a, b\in\mathbb{C}$ and $|a|^2 + |b|^2 = 1$. Now, I would like to take $a = \frac{1}{\sqrt{2}}(1 +...
14
votes
4answers
1k views

Are there more entangled states or non-entangled ones?

I'm trying to understand entanglement in terms of scarcity and abundance. Given an arbitrary vector $v$ representing a pure quantum state of, say, dimension 4, i.e. $v \in \mathcal{H}^{\otimes 4}$, ...
-2
votes
0answers
26 views

Imaginary part in calculation [closed]

I want to simulate (I use mathematica) a matrix that has imaginary number. Given the matrix, $$A = \begin{pmatrix} e^{2I+3}Sin{(2\Pi t)} & e^{I (\Pi)}Cos{(2\Pi t)} \\ Cos{(2\Pi t)} & -e^{...
0
votes
1answer
31 views

What does it mean to say exchange “force” is not really a force?

If I understand it a bit the standard answer for this is: the pushing/holding apart of fermions and the pulling/holding together of bosons is just a result of symmetrization requirement (Griffths' ...
0
votes
1answer
43 views

Quantization of energy in semi-infinite well

Consider an electron with total energy $E>V_2$ in a potential with $$V(x)= \begin{cases} \infty & x< 0 \\ V_1 & 0< x< L \\ V_2 & x>L \end{cases} $$ ...
0
votes
0answers
22 views

Time-dependent perturbation theory [closed]

In time dependent perturbation theory there is a group of states having energies nearly equal to initial state.what will be time dependence of probability of finding system in any of such state? Plz ...
-1
votes
1answer
24 views

What magnetic quantum no. Actually represent? [closed]

If azimuthal quantum no. i.e l=3 then magnetic quantum no be -3,-2,-1,0,1,2,3. What does it represent?
-1
votes
1answer
70 views

What is limitation of Pauli exclusion principle? [closed]

According to Pauli "no two electrons in an atom can have the same values for all the four quantum numbers" but if we take any atom with $n=2$ and its 2nd subshell i.e 2p(that contain 3 orbitals) ...
1
vote
1answer
63 views

Schrödinger's Equation with multi-part potential

I have this potential $$V(x) = \left\{ \begin{array}{ll} \infty & \mbox{if } x < -a \\ \frac{V_o}{a}x & \mbox{if } -a \leq x \leq a \\ V_o & \mbox{if } x \geq a \ \end{...
4
votes
5answers
110 views

Is it a coincidence that quantum harmonic oscillators and photons have energy quantised as $E=hf$?

I have studied the quantum harmonic oscillator and solved the Schrodinger equation to find the eigen-energies given by $$ E_n = \left(n+\frac{1}{2}\right)\hbar \omega. $$ Which means the energy ...
5
votes
1answer
68 views

Which charge to use in the Dirac quantization condition?

I have a follow-up question to Dirac magnetic monopoles and quark fractional electric charge quantization, regarding whether the "unit of electric charge" in the Dirac quantization condition should be ...
0
votes
0answers
29 views

Entangled particles information transfer

No-communication theorem forbids the transfer of information using entangled particles. But does it implies that information does not pass between the entangled particles themselves? Is there a ...
5
votes
2answers
113 views

Wouldn't the thermodynamic cost of creating alternate universes make the Many Worlds interpretation implausible?

I was thinking about the many interpretations of quantum physics, and one thing that never made sense to me was the many world's interpretation. Basically at any given moment for which something ...
2
votes
1answer
82 views

GR says that time and space are aspects of the same thing, yet there is no observable for time in QM

I understand that the topic of a time operator in quantum mechanics has come up more than a few times so forgive me if this is a repeat question but I couldn't find anything specific to my question. ...
2
votes
2answers
150 views

Eigenvalues of Hermitian operators are real and the dependence/independence of boundary conditions

Without reproducing proofs: Eigenvalues of a Hermitian operator are real (proof does not rely on the boundary conditions). The momentum operator is Hermitian (proof does not rely on the boundary ...
-2
votes
0answers
49 views

Mathematical method of Physics [closed]

Please any one can tell me how to get lecture of mathematical method of physics complete course online download complete lecture series. Which professor best for this subject please guide me how to ...