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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Variational principle perturbation

I am trying to learn 2D SHO and free particle variational principles. However, I came across a perturbation like so: $Ax^2y^2$. The particle is simple harmonic in $x$ and a free particle in $y$? I'm ...
2
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0answers
63 views

Quantum mechanical monopole [duplicate]

Recently in physics news, scientists have experimentally discovered the so-called quantum mechanical monopole. It seems that a quantum mechanical monopole is different from a magnetic monopole. So my ...
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47 views

my car is overheating after I just fixed the water pump? [on hold]

Steam coming out the Cool lit jug.. my engine shaking. Also my exhaust pipe throwing Water vapor out. I just changed the water pump..
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0answers
34 views

Are there any event-based interpretations of quantum physics? [on hold]

Are there any interpretations of quantum physics where we have a combination of probabilities and objective realizations of these probabilities on a very low level. The first part of my question is ...
2
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0answers
32 views

Understanding quantum coherence in biological processes (Magnetoreception)

Moved my questions to the top. Context below. Why is the strength of the electric field and the coupling constant being compared to the inverse coherence time? What is the inverse coherence time? Is ...
2
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0answers
25 views

Toric Code and the String-Net Model

What, exactly, makes the toric code a quantum error-correcting code as opposed to any other string-net model? What makes it special? The way I understand it, it's a normal string-net model on a torus, ...
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0answers
11 views

Second-order correction in Quantum-Confined Stark effect

In the wikipedia article, there is a second-order correction in the Quantum-Confined Stark Effect. I could not understand how it was solved. I did not understand the meaning of 2(0) and 1(0) and how I ...
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0answers
18 views

Isotropic 3D oscillator excitation levels in different eigenket basis

An isotropic 3D oscillator's excitations can be represented by combinations of raising operators $\hat{a}_i^{\dagger}$ acting on the vacuum $|0,0,0\rangle=|0\rangle$ in the $x,y,z$ basis, but also ...
2
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2answers
41 views

How do you find the projection operator onto an eigenspace if you don't know the eigenvector?

I was working on exercise 2.60 of Nielsen-Chuang which is as follows: Show that $\vec{v}\cdot\vec{\sigma}$ has eigenvalues $\pm 1$, and that the projectors onto the corresponding eigenspaces are ...
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0answers
17 views

Quantum Monte Carlo for harmonic oscillator

I'm trying to calculate harmonic oscillator using quantum monte carlo (path integral and metropolis algorithm). It's one particle in harmonic potential. I know the theory. One divides the partition ...
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0answers
29 views

Why don't wavefunctions for electrons in neighbouring molecules overlap?

I've come across this picture of two linked molecules. The intramolecular distances look similar to the intermolecular distances and it seems like that will be the case however you draw it because of ...
1
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1answer
35 views

Normalizing a wave function in a mixed well

So I got this potential and want to solve for the even wavefunctions http://imgur.com/GKAy4nD Since it's symmetric around the origin I need only to look at the interval [0,b] and solve for the ...
2
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1answer
46 views

Can I Weyl-order the following Hamiltonian?

I am trying to perform a path integral but I am having trouble with the Weyl ordering of my Hamiltonian. The Lagrangian of the system in question is $$L~=~\frac{1}{2}f(q)\dot{q}^2,$$ where $f(q)$ ...
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0answers
60 views

Why isn't everthing in a superposition state? [duplicate]

I know that a superposition is a state in which there are 50% and 50% (other % also) chances of two things to happen so why am I not in a superposition state? Example, I am at rest and i now choose to ...
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2answers
54 views

Why can't a classical bit behave like a qubit?

For example i have a 2 qubits which can have 4 possibilities i.e. 00, 01, 10, 11 so this shows that the 2 qubits can contain four bits of information as they are superpositioned but i think 2 ...
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0answers
77 views

Symmetries and quantum numbers $n$, $l$, $m$, $s$ [on hold]

I would like to better understand the symmetries and groups underpinning the quantum numbers $n,l,m,s$ for a bound electron. My understanding is that: $n$ is the principal quantum number, and is ...
1
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0answers
43 views

When trying to see what symmetries an operator generates, how do you “decide” what coordinate to apply it to?

Suppose I have $\hat{O}_{1}=-i\hbar\partial_{x}$ then \begin{eqnarray} e^{-i\gamma\hat{O}_{1}/\hbar}x\,e^{i\gamma\hat{O}_{1}/\hbar}=x+\gamma \end{eqnarray} and \begin{eqnarray} ...
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0answers
34 views

Role of Hilbert Space in physics [duplicate]

Why in quantum mechanics do we require that the state space be a Hilbert space rather than just an inner product? Does the completeness of the norm have any clear physical role?
2
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1answer
32 views

Notation of angular momentum operators vs numbers

I'm reading about finding the mass of quarks in mesons. In the lecture notes, it says We need to find $\langle\boldsymbol{s}_q\cdot\boldsymbol{s}_\bar{q}\rangle$. Since $L=0$, then ...
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0answers
24 views

Why doesn't the electron fall into the nucleus? [duplicate]

Electrons move around the nucleus, which contain protons and neutrons. I know that quantum mechanics tells us that the nucleus is made up of fundamental particles, but why (quantum mechanically ...
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0answers
25 views

What is a state vector? [on hold]

Please can someone give me an intuitive expansion of a state vector? For example, what are they, functions? What does one state vector represent? One does it mean to add two state vectors? etc. I have ...
1
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1answer
22 views

Multiply creation operator by a phase factor

A basic question, but I'm not completely confident what I'm doing is legit. I can multiply a creation operator by an arbitrary phase factor and it doesn't change any physics. True? I have a ...
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2answers
70 views

Meaning of the Angular Momentum in Quantum Mechanics

There was a discussion about the angular momentum in QM in an online course that I am attending now. The discussion and the answers did not satisfy me so I wanted to ask it on Physics SE. In the ...
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1answer
23 views

Is post selection a quantum effect?

Suppose I have two bits $x$ and $y$ and a map $M:x,y \to x \veebar y,x \veebar y$ where $x,y$ $\in \{0,1\}$ and $\veebar$ stands for bit xor. If I post-select the case where the output is $x^{'}=0 , ...
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1answer
39 views

Angular Momentum Expectation Values in Spherical Coordinates

I have a homework problem that asks: Using the spherical harmonics calculate $\langle J_x \rangle$, $\langle J_y \rangle$, $\langle J_z \rangle$ in the state $|l,m\rangle$. Use the derivative ...
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1answer
42 views

Compatible Observables and Measurement

Suppose $A$ and $B$ are compatible observables (i.e. $[A,B] = 0$). We take the eigenkets of $A$ to be $|a_1 \rangle \ldots |a_N \rangle$. Further, we suppose that the first $k$ eignekets of $A$ are ...
2
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2answers
64 views

Transition from 4-potential to E and B [on hold]

In my lecture notes there is a step that i cannot follow: $$\frac{i}{2}[\gamma^{\mu},\gamma^{\nu}] (\partial_{\mu}A_{\nu}-\partial_{\nu}A_{\mu})=: \sigma^{\mu\nu}F_{\mu\nu}=i\vec{\alpha} ...
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0answers
16 views

why does the spaceship stand still in the bubble while movement is taking place outside? [on hold]

The question concerns travel faster then the speed of light.Another quesion conecerning the colour in the front being bler och the colour in back being redder. How it possible just these two colours ...
3
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1answer
66 views

Time Evolution of Position Operator

I am trying to understand why $$e^{-it\triangle}xe^{it\triangle}=x-2it\nabla$$ where $x$ is just multiplication operator by $x$. In particular, the text says this can be seen by differentiating with ...
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0answers
27 views

What is the reason for 2 qubits no longer being entangled after interaction with a causality violating qubit?

Background : I was reading the following paper on closed timelike curves ( CTC ) : Quantum Mechanics Near Closed Timelike Curves. The Deutsch consistency equation for CTC is $$\rho_{CTC}=Tr_{CR}( U ...
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0answers
24 views

p-adic and quantum mechanics [duplicate]

In physics we call integer based quantity as “quantization”, so you have energy, momentum etc taking quantized values. But in math, this kind of situation is really the age old problem of number ...
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1answer
37 views

Derivation of Pauli Hamiltonian

In my lecture notes there is a step that i cannot follow: $$\frac{i}{2}\epsilon_{ijk}\sigma_k [\pi_i,\pi_j] = -e\epsilon_{ijk}\partial_iA_j\sigma_k$$ with $\vec{\pi}=\vec{p}-e\vec{A}(x)$ When I ...
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1answer
36 views

What are the units of the creation and annihilation operators?

The creation and annihilation operators - also known as ladder operators are; $ \hat{a}^\dagger$ and $\hat{a}$ respectively. Using the equation $\hat{H} = \hbarω\left(\hat{a}^\dagger \hat{a} + ...
3
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2answers
177 views

What exactly implies the need of quantum mechanics for self-adjoint and not only symmetric operators? [duplicate]

We know that quantum mechanics requires self-adjoint operators, not only symmetric. Can we say that this follows ONLY from the two following axioms of quantum mechanics, namely that each observable ...
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0answers
24 views

Is quantum superposition an actual, physical phenomenon? [duplicate]

Correct me if I'm wrong, but I'm given to understand that the intention of Shrodinger's thought experiment was to point out the folly of the Copenhagen interpretation, in that a quantum particle being ...
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0answers
32 views

Ladder Operator proof

I was wondering what the proof was that a ladder operator will generate all the eigenenergies for a system. e.g. the QM harmonic oscillator. So after manipulating the ladder operator we get; ($a$ is ...
2
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0answers
33 views

joint probability distribution in QM

The problem of incompatible observables in quantum mechanics is often explained in terms of their (self-adjoint) operators having different sets of eigenstates. This causes their commutator to be ...
1
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1answer
41 views

Recurrence differential equations

We all know recurrence equations like e.q. Fibonacci relation $$F_{n} = F_{n-1} + F_{n+1}$$ In order to find general expression for any $n$, we can use generating function method $$G(x) = ...
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0answers
20 views

Can any experiments NOT be done through the classic control-experimental groups method? [on hold]

The classic control-experimental groups method involves having a control group to measure what happens when everything is regulated, and then one or more experimental groups are used, each having one ...
0
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1answer
92 views

Quantum violation of Newton's Third Law? [on hold]

From this site: http://www.learning-mind.com/5-thought-provoking-quantum-experiments-showing-that-reality-is-an-illusion/ I gained the knowledge that a group of scientists, upon measuring a tiny ...
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0answers
18 views

Quantum dual-slit experiment via Youtube live streaming (explanation within)?

What will happen with this theoretical setup: A scientist is bored one day and positions his photon detector at the classic dual-slit photon experimental setup. Then he wires the photon detector up to ...
2
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3answers
147 views

Deriving cross product from angular momentum algebra

Is it possible to derive: \begin{equation} \hat{L}=\hat{r}\times \hat{p} \end{equation} from the angular momentum algebra: \begin{equation} [\hat{L}_i,\hat{L}_j]=i\ \hbar\ \epsilon_{ijk}\hat{L}_k\ ? ...
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0answers
47 views

Density matrix in Quantum Statistical Mechanics

What is the connection between the density matrix in quantum statistical mechanics and the probability of being a particular state in classical statistical mechanics? It would seem that the elements ...
1
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1answer
48 views

BB84 protocol what do they do once they have the key?

In the BB84 protocol Alice and Bob share a key via a method using both quantum and classical channels. I understand how they do this. But I don't understand what they then do with the key? I.e. How do ...
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1answer
34 views

Calculation & derivation of de-Broglie wavelength [duplicate]

How to calculate the de Broglie wavelength of an $\alpha$ particle that is accelerated through a potential difference of $V$ from rest.
10
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4answers
595 views

Can dimension analysis be used in developing more advanced physics equations?

It is obvious that dimensional analysis can be used to derive many classical mechanics equations (excluding constants). As long as all the dependent quantities are known. My question is whether this ...
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0answers
37 views

Solutions to Dirac equation in 2+1 D [on hold]

Hello I solved the Dirac equation in 2+1 D taking two different gamma matrix representations. rep.A: $$\gamma^0=\sigma^3, \qquad\gamma^1=i\sigma^1, \qquad\gamma^2=i\sigma^2.$$ rep.B: ...
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0answers
23 views

How do I know the limit for the calculation of normalized wave function.

Let we have a eigen function for dumbbell ball given which is $ \phi= A e^{i x}$ and I have to determine the normalization constant A. I know in thios case I will have to write $$\int \phi \phi^* ...
2
votes
2answers
39 views

Why does the raising operator, when acting on a ket with a maximum second quantum number, yield zero?

I'm studying the general formalism of angular momentum in quantum mechanics from Zettili's "Quantum Mechanics: Concepts and Applications", and came across the following equation (labeled 5.37) on page ...
3
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2answers
81 views

Perturbation theory in quantum harmonic oscillator [on hold]

This question concerns the quantum harmonic oscillator: (a)Express the operator $\hat B = \hat x \hat p + \hat p \hat x + \hbar$ in terms of $\hat a_{\pm}$ and $\hbar$ (b)Write the matrix ...