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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2answers
587 views

Discovery of $E=hf$?

How was the equation $E=hf$ discovered? Was the proportional expression between energy and frequency of light $E\propto f$ discovered only by experiment? Or is there some logical(theoretical) senses ...
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6answers
2k views

What happens when a photon hits a beamsplitter?

Yesterday I read that we can affect the path and the 'form' (particle or wave) of a photon after the fact (Wheeler's delayed choice experiment). Part of what is puzzling me is the beam-splitter. Are ...
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2answers
4k views

Physical interpretation of normalization of wave fuctions

Does normalization of wave function mean that we are getting our state vector to unit length? If that's the case what does it mean physically? Also is the underlying vector space finite dimensional? ...
5
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3answers
3k views

Momentum of particle in a box

Take a unit box, the energy eigenfunctions are $\sin(n\pi x)$ (ignoring normalization constant) inside the box and 0 outside. I have read that there is no momentum operator for a particle in a box, ...
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1answer
397 views

Hamiltonian reduction having constant of the motion

I have this $2^n*2^n$ matrix that represent the evolution of a system of $n$ spin. I know that I can have only one excited spin in my configuration a time. (eg: 0110 nor 0101 ar not permitted, but ...
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0answers
122 views

Number theoretical function applied in physics? [closed]

I have a series of number theoretic phenomena (mathematics) that I can describe exactly by the superpositions or linear combination of the below function (I know it is an inverse Fourier type). Does ...
1
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2answers
2k views

Do excited electrons drop back to same quantum state?

I'm trying to wrap my head around spectroscopy, therefore, I am looking for as complete an answer as possible here, hence why I have broken the question into a different points. Here is what I know ...
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2answers
200 views

Molecular Hamiltonian

I was reading some material on the Molecular Hamiltonian on Wiki. It said that, Almost all calculations of molecular wavefunctions are based on the separation of the Coulomb Hamiltonian first ...
2
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1answer
131 views

One body harmonic oscillator states expressed in terms of creation operators

I am reading trough chapter one of Moshinsky's "The harmonic Oscillator in Modern Physics". However i am having some trouble with the mathematics in section 8 of chapter 1. I will sketch a summary of ...
5
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1answer
234 views

Quantum Mechanical Effects of an object accelerating near speed of light $c$?

Consider a space ship, undergoing constant acceleration (which for our purposes means that the same amount of energy is being used per second to increase its speed). According to special relativity ...
1
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1answer
126 views

Incompatibility of GR and QM [duplicate]

I am told that the theories of General Relativity and Quantum Mechanics are fundamentally incompatible... Why is that? Someone explained that it had to do with the fact that quantum particles such As ...
3
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1answer
200 views

Path integral formulation understanding [duplicate]

I have done basic quantum mechanics and now I want to do the path integral formulation. I find Feynman's book Path Integrals in Quantum Mechanics difficult. Is there an easier alternative?
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2answers
104 views

Quantum Mechanics, Uncertainty Principle— help understanding notes

There is a section of my notes which I do not understand, hopefully someone here will be able to explain this to me. The notes read (after introducing the uncertainty operator): If the state $...
2
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1answer
327 views

Harmonic oscillator - wavefunctions

I understand now how I can derive the lowest energy state $W_0 = \tfrac{1}{2}\hbar \omega$ of the quantum harmonic oscillator (HO) using the ladder operators. What is the easiest way to now derive ...
0
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1answer
123 views

Is this hypo-theoretical model of future prediction feasible? [closed]

First let me state that I am not, nor ever have I been, a physics student. I am working on an idea for a book I'm writing. This is a thought experiment that posits the existence of a computer system ...
0
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2answers
232 views

Quantum Mechanical Interpretation of Water Waves?

So I have been exploring the idea of wave-particle duality and came across and interesting idea. Could water waves, be interpreted as particles in some context? If so, how would you observe their ...
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3answers
113 views

What is the most general unitary that commutes with a one dimensional projector in a finite dimensional Vector Space

Given a Hilbert space of finite dimension $N$ with an orthonormal basis $\mathcal{B}=\{|0\rangle,\ldots,|N-1\rangle \}$ what is the most general unitary operation that commutes with the projector onto ...
0
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2answers
85 views

QM the superposition principle

In Zetilli's book author says that we can interpret an inner product $\langle x | \psi(t) \rangle$ as a wave function $\psi (x,t)$ and i understand this. Next he talks about how a state of the system ...
3
votes
1answer
130 views

Path integral representation of $\langle q_f t_f|p(t_1)|q_i t_i\rangle $

How do I calculate path integral representation of $\langle q_f t_f|p(t_1)|q_i t_i\rangle $ where $t_i<t_1<t_f$? I am doing this by discretizing, the time intervals and adding a complete set of $...
4
votes
1answer
415 views

Calculation of the spherical harmonic sum in the propagator of the particle on a sphere

I am calculating the propagator of the free particle on a sphere : $K(\theta_f \phi_f t_f; \theta_i \phi_i t_i)$. The wavefunctions in this case are the spherical harmonics $Y_{lm}(\theta, \phi)=\frac{...
0
votes
2answers
628 views

Quantum tunneling and a football permeating a wall

I was wondering if I can say to a layman that "upon throwing the ball on a wall an enormously large number of times, there is a small probability that the ball will go through the wall", while ...
2
votes
0answers
119 views

How can any QM interpretations which use a linear Schrödinger Equation be used to quantitize gravity?

Since general relativity is nonlinear, how could we quantitize gravity with QM interpretations which use the linear Schrödinger Equation? Or is this fundamentally unworkable?
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1answer
296 views

How to interpret temporal coherence in Young's double slit experiment with single photons?

I have a problem with understanding what is the role of coherence in such experiment. Taking the Dirac's statement that photon interferes only with itself, it's fairly understandable, that single ...
1
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1answer
439 views

Super High Frequency Electromagnetic Radiation - String Theory

I am a serious high school student with one year of physics class experience, so please point out if there are any flaws in my question or reasoning. Thanks! Gamma ray radiation possesses a ...
3
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4answers
3k views

Can Newton's laws be explained by Quantum Physics? [duplicate]

I have only basic knowledge of physics. Could you please explain to me if a "Quantum" laws can theoretically (perhaps in the future?) be used to explain everything in macro levels? I'm having ...
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2answers
3k views

From position space to momentum space

Lets say I have a state vector $\left|\Psi(t)\right\rangle$ in a position space with an orthonormal position basis. If I now use an operator $\hat{p}$ on this basis I will get basis which corresponds ...
0
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0answers
52 views

the effects of an ln-prime transformation to physical models

I have rather a "toy" type of modelling-problem that appeared to me along a book I am writing on number theory. I would be outmost thankful for any concrete or inspirational answers, including ...
4
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2answers
3k views

Deriving the Angular Momentum Commutator Relations by using $\epsilon_{ijk}$ Identities

I've been trying to derive the relation $$[\hat L_i,\hat L_j] = i\hbar\epsilon_{ijk} \hat L_k $$ without doing each permutation of ${x,y,z}$ individually, but I'm not really getting anywhere. ...
5
votes
1answer
482 views

Clarification of Landauer approach

I am trying to understand the Landauer approach. Consider the setup: (left contact)-(conductor)-(right contact). For simplicity, the conductor is a 1d wire (the transverse part is not relevant for ...
5
votes
1answer
2k views

Why we call the ground state of Kitaev model a Spin Liquid?

Now we always talk about the so-called Kitaev spin liquid. One important property of spin liquid is global spin rotation symmetry. Let $\Psi$ represents a spin ground state, if $\Psi$ has global spin ...
3
votes
1answer
251 views

Diagonalizing/eigenvalues of the infinite dimensional matrix of N harmonic oscillators on a ring

I have trying to show that the continuum limit of N quantum harmonic oscillators gives rise the the klein-gordon field. However, instead of a usual finite string, I want to do it on a ring. Hence, my ...
2
votes
2answers
252 views

Was TP Singh right to say that a theory of quantum gravity necessitates the Copenhagen Interpretation?

http://iopscience.iop.org/1742-6596/174/1/012024 In the above link we see TP Singh arguing that only Copenhagen will work for a theory of quantum gravity. Some of his key points are "quantum theory ...
6
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0answers
161 views

Quantization as a functor [duplicate]

Can anyone give an mathematical elaboration of the following statement: Quantization is a functor carrying the category of Hilbert space and linear maps to that of Symplectic manifolds satisfying ...
1
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1answer
276 views

Anti-particle problem for Dirac sea

According to the Dirac hole theory we know that Dirac sea is completely filled with negative energy, called vacuum. We will need $2mc^2$ or greater to get electron and a positron by incident photon. ...
14
votes
3answers
1k views

Meaning of inner product $\langle \vec{r} | \psi(t)\rangle $

I have come across the equation which comes out of the nothing in Zettili's book Quantum mechanics concepts and applications p. 167: $$\psi(\vec{r},t) ~=~ \langle \vec{r} \,|\, \psi(t) \rangle.$$ ...
5
votes
3answers
768 views

How can particles travel in a straight line?

A particle can be set off in a certain direction by giving them momentum. Momentum is a vector, so the particle heads off in a specific direction. But the wave function of the particle allows it to ...
16
votes
3answers
3k views

Origin of Ladder Operator methods

Ladder operators are found in various contexts (such as calculating the spectra of the harmonic oscillator and angular momentum) in almost all introductory Quantum Mechanics textbooks. And every book ...
1
vote
2answers
192 views

Expectation value - Zetilli vs Griffith

I know that an inner product between two vectors is defined like: $$\langle a | b\rangle = {a_1}^\dagger b_1+{a_2}^\dagger b_2+\dots$$ but because a transpose of a component for example $a_1$ is ...
3
votes
1answer
146 views

Observables - what are they?

I often read in books that an observable is represented by an Hermitean operator. But it is deceiving as operator isn't the observable. As far as I've read the observable is denoted like $\langle \...
1
vote
2answers
496 views

Wigner characteristic function

I came across the "representation of a Gaussian state by its Wigner characteristic function". I don't know what Wigner characteristic function is and google results are not precise enough. Neither ...
1
vote
1answer
161 views

Geometrical Representation Grover algorithm

I am studying the Grover algorithm and in my and others lectures, I've come across this picture. If the dimension of the computational basis is greater than 2, why does the evolution algorithm ...
0
votes
1answer
90 views

Why Quantum correlation is not uniform in this diagram?

Following diagram is from a Wikipedia article which shows Quantum Correlation for local hidden variables and Quantum Mechanics and experiments confirm Quantum Mechanics predictions. My question is ...
2
votes
0answers
57 views

Is it possible to detect subjective decoherence? If yes, how?

In his paper from 1994 Thomas Breuer describes a phenomenon of subjective decoherence (p. 43). I wonder whether it can be measured, and if yes, how. I also wonder whether it would allow to create an ...
16
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0answers
227 views

Anyons as particles?

I'm trying to understand the basics of anyons physics. I understand there is neither a Fock space they live in (because Fock is just the space of (anti-)symmetrized tensor product state, see e.g. ...
7
votes
2answers
1k views

Is particle entanglement a binary property?

Is the particle entanglement a boolean property? That is, when we consider two given particles, is the answer to the question "are they entangled" always either "yes" or "no" (or, of course, "we are ...
0
votes
2answers
2k views

Using the Normalization Condition with Wavefunction

I'm very confused with this problem and I was looking for some guidance. $$\psi(x) = Ae^{ikx}e^{-x^2/2a^2}$$ Use the normalization condition to find A. So I understand that you use the normalization ...
1
vote
1answer
80 views

Can a link between photons that don't exist at the same time provide communication with the past?

They have published something about a link between photons that don't exist at the same time. Does this means that it is possible to build a device that will receive messages from itself but these ...
4
votes
2answers
617 views

How do you come up with a POVM?

This is a made-up example, just to understand a concept. If changing the probability values aids your explanation, that's fine by me. Say you have a physical quantity $E$ that can take values 1, 2, 3 ...
0
votes
1answer
111 views

Frank Hertz experiment and different jumps

Why is it assumed that in this experiment, the jump will be between the second and the first states. Couldn't it be that when the electrons have enough energy, an atom absorbs enough to get to the ...
2
votes
1answer
185 views

Time evolution of a quantum state

I have another point in QM that I would like clarified. Suppose $$\{|n\rangle\}$$ is a set of eigenstates of both the Hamiltonian $H$ and another operator $\hat O$ corresponding to an observable also. ...