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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1answer
324 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 ...
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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 ...
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2answers
225 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 ...
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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
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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
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1answer
409 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, ...
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2answers
608 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 ...
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0answers
117 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
279 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
427 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 ...
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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 ...
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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
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1answer
472 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
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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
246 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
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2answers
249 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 ...
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0answers
160 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
268 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. ...
13
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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: $$\psi(\vec{r},t) ~=~ \langle \vec{r} \,|\, \psi(t) \rangle.$$ ...
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3answers
724 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 ...
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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 ...
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2answers
191 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
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1answer
142 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 ...
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2answers
473 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
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1answer
159 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
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1answer
89 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 ...
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0answers
56 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 ...
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0answers
201 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
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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
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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 ...
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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
598 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
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1answer
107 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
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1answer
184 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. ...
7
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1answer
473 views

Differential equation (Greens function) satisfied by the kernel using path integrals

I'm reading Feynman and Hibbs, Quantum Mechanics and Path Integrals. How do I show that the kernel $$\tag{2-25} K(x_2 t_2;x_1 t_1)=\int e^{\frac{i}{\hbar}S[2,1]}\mathcal{D}x$$ satisfies the ...
3
votes
1answer
185 views

Can we apply de Broglie's relations to sound waves?

Can we apply the de Broglie relations to a sound waves ? Is it possible? if yes how do you do that? what would be the mass(m) in the equation?
2
votes
2answers
50 views

Clarification on measurement in QM

Supppose we are given a quantum state that isn't pure state, such that it is a linear combination of the eigenstates of a Hermitian operator $\hat O$. $$|\psi\rangle=N\sum \alpha_i |i\rangle$$ where ...
4
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1answer
560 views

Quantum Field Theory and Hilbert space dimensionality

Much (All?) of quantum theory can be done in separable Hilbert spaces with a countable basis. How about quantum field theory? Is it “quite happy” (mathematically consistent) if everything is ...
7
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1answer
592 views

Hilbert space of a free particle: Countable or Uncountable?

This is obviously a follow on question to the Phys.SE post Hilbert space of harmonic oscillator: Countable vs uncountable? So I thought that the Hilbert space of a bound electron is countable, but ...
3
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1answer
153 views

Trying to understand mixed states

I took a basic quantum chemistry course (McQuarrie's "Quantum Chemistry"), but it never dealt with mixed states -- only pure states (or if it did, we never got to it in class). So I'm trying to ...
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17answers
5k views

Quantum mechanics and everyday nature

Is there a phenomenon visible to the naked eye that requires quantum mechanics to be satisfactorily explained? I am looking for a sort of quantic Newtonian apple.
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2answers
1k views

Interpretation of de Broglie wave

Until what point can the de Broglie wave be thought as a real wave? I mean, is it made of something? What amplitude does it have? Is it a sine wave? How can it be related to the wavefunction of the ...
7
votes
1answer
240 views

What is the reason that relativistic corrections for hydrogen atom work?

Here I cite part from Sidney Coleman's lectures on Quantum Field Theory: It is a phenomenal fluke that relativistic kinematic corrections for the Hydrogen atom work. If the Dirac equation is used, ...
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2answers
504 views

Calculating the the kernel using path integrals for quadratic lagrangians

I am reading Feynman and Hibbs on Path Integrals. In section 3.5, they show that the kernel for a lagrangian of the form $L=a(t)\dot{x}^2+b(t)\dot{x}x+c(t)x^2+d(t)\dot{x}+e(t)x+f(t)$ is ...
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0answers
87 views

fast quantum random number generator + limited decoherence rate => Schrödinger cat state?

Suppose that fast quantum random number generator (QRNG, https://qrng.physik.hu-berlin.de/) is placed in a subsystem which has limited interaction with the rest of the world. What would happen if ...
0
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1answer
89 views

Eigenvector Grover Operator

I have a question about the eigenvectors for the evolution operator of Grover's algorithm. Let $U=R_DR_f$, where $$\begin{align*} R_D &= 2|D\rangle\langle D| -I_N , \\ R_f &= ...
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1answer
96 views

Eigenvalue $a_n$

Q1: In Zetilli's book page 166 (ch. "Postulates of QM", eq. 3.1) i encountered an expression $\hat{A}|\psi\rangle = a_n|\psi_n\rangle$. I know this is an eigenvalue equation, but i have seen another ...