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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119 views

A few questions on wave packets and uncertainty relations

According to Cohen-Tannoudji the wave-function for a one-dimensional free particle can be written as $$ \psi (x,0)=\frac{1}{\sqrt{2 \pi}} \int g(k) e^{ikx} dk.$$ While $g(k)$ is not specified, there ...
2
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2answers
32 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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1answer
55 views
+50

Blackbody cavity relationship between energy of oscillators and EM radiation

This question is based on Planck's view of blackbody radiation in a cavity. Here is a quote from here: ...where $\langle E \rangle$ is the average energy of the oscillators present on the walls of ...
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1answer
111 views

Does a normal torch emit entangled photons?

I was reading a sciencenews.org post about three photons being entangled. My question here is, why is the chance of producing an entangled pair once in a billion times? Isn't every particle produced ...
4
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1answer
170 views

Poles for a particle scattered in a delta potential

I am working on problem a professor gave me to get an idea for the research he does, and have hit a point where I'm having a difficult time seeing where I need to go from where I'm at. I would also ...
3
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2answers
276 views

Hydrogen atom: potential well and orbit radii

I happened to open up an old solid-state electronics book by Sah, and in it he says: "it is evident that the electron orbit radius is half the well radius at the energy level En" The orbit radius is ...
2
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1answer
1k views

Time-reversal symmetry

For a quantum system with time-reversal symmetry, other than the absence of a magnetic field, can we infer anything else about the system?
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0answers
31 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
60 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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0answers
17 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 ...
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0answers
45 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..
2
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1answer
80 views

Proper way to quantize the string in the light-cone gauge

In many books like Polchinski and Green-Schwarz-Witten the light cone quantization is carried out in a fast way. They just use the virasoro constraint in the light-cone gauge to get the ligh-cone ...
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 ...
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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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3answers
180 views

Measurement of quantum state

Consider a particle in a box system. Assume its state to be a superposition of the ground and the first excited energy states. Consider two observers A and B (rest of the world). A made the ...
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4answers
472 views

Quantum Mechanics [on hold]

Quantum Mechanics. Could anyone help me to understand the concept involved? Double slit experiment can be easily understood by Wave nature of light, but while explaining it with photons, it required ...
2
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0answers
24 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
10 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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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 ...
11
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2answers
493 views

Are Thomas Breuer's subjective decoherence and Scott Aaronson's freebits with Knightian freedom the same things in essence?

In his remarkable works (1,2 and their recent development 3) Thomas Breuer proves by diagonalization the phenomenon that the observer cannot distinguish all phase space states of a system where he is ...
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0answers
76 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 ...
2
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1answer
45 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
15 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
28 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 ...
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2answers
53 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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1answer
52 views

Hamiltonian symmetry Lie algebra

What is the connection between complete set of commuting observables and generators of the Lie group? I have a Hamiltonian written down in second quantized formalism and I also checked that it ...
1
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1answer
130 views

Quantum simple harmonic oscillator interpretation

I am just wondering what does the SHO system from quantum mechanics actually physically represent? Is it just a SHO of a quantum particle, seems a little too obvious for quantum theory? I'm from a ...
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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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1answer
134 views

Difference between expectation values of $L^2$, $L_z$ and measuring $L^2$, $L_z$

I was given with this hydrogen radial wavefunction $$ R_{21} =\left(\sqrt{\frac{1}{3}}Y^0_1 + \sqrt{\frac{2}{3}}Y^1_1\right) $$ and was asked to find a) What are the expectation values of the ...
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
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?
3
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1answer
242 views

What is the Philosophy Behind Relational Quantum Mechanics?

I watched this video on Relational Quantum Mechanics yesterday and my brain has been trying to comprehend it since. The interpretation I currently have is this: If an observer O measures the state S ...
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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
24 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 ...
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1answer
21 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 ...
1
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1answer
877 views

Stark effect in two level atomic, laser-driven system?

In a two level atomic system (Rabi oscillating problem) the perturbative potential is oscillating / sinusoidal because it comes from the electric field from the laser. Now stark effect is the ...
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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 ...
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1answer
38 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
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
36 views

Confusion about Shankar 1D Scattering in a Single-Step Potential

Section 5.4 of Shankar studies the problem of a single-step potential where $$V(x) = \begin{cases}0&x<0\\V_0 &x>0\end{cases}.$$ It was shown that a incident Gaussian packet $$\psi_I(x,0) ...
3
votes
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 ...
2
votes
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} ...
-1
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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 ...
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0answers
26 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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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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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
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 ...
2
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2answers
116 views

How do probabilities emerge in the many-worlds interpretation?

My understanding is that at each quantized unit of time that a split occurs, every possible recombination of particles occurs in the 'objective' universe. If this is the case, what relevance to ...
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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} + ...