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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Naive interpretation of Galilean invariance of the TDSE

I was told today by someone smarter than myself that the time-dependent Schroedinger equation in one dimension was invariant under a Galilean transformation of $(x,t)$, namely under ...
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349 views

Why is Wheelers Delayed Choice Experiment Incorrect?

I have come across 'Wheelers Delayed Choice Experiment' which tries to prove that you can work out which Slit a Photon Goes Through in the Double Slit Experiment. But I thought it was impossible to ...
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56 views

Is operator $\hat{O}_{\alpha}:|\phi,\psi\rangle\mapsto |e^{i~\alpha[\phi,\psi]}~\phi,e^{-i~\alpha[\phi,\psi]}~\psi\rangle$ unitary?

Is the operator $\hat O_{\alpha}$ which is defined in the following a unitary operator? Operator $\hat O_{\alpha}$ is supposed to act on composite states with two explicit components, such that ...
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Rotational wave funtion of a nucleus

The rotational hamiltonian of an axially symmetric rotor is, in the intrinsic frame of the body, where the moment of inertia is diagonal, $$\mathcal{H} = \frac{\hslash^2}{2I} \left(J^2 - I_3^2\right) ...
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58 views

How does an operator transform under time reversal?

We know that a time-reversal operator $T$ can be represented as $$T=UK$$ where $U$ is some unitary operator and $K$ is the complex conjugation operator. Then under time-reversal operation, a quantum ...
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38 views

Can a two-levels photon pair be created either entangled or not entangled? [closed]

I am learning about experiments on Quantum Optics and Quantum Tomography in order to understand how to measure two qubits with an arbitrary quantum state of their polarization degrees of freedom. ...
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42 views

Proof of Kohn's theorem

In 1961 W. Kohn's paper ( Phys. Rev. 123, 1242 (1961) ) first stated that the electron-electron interaction does not change the cyclotron resonance frequency in a bulk three dimensional gas. I can ...
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124 views

Quantum Spin Simulation

In Leonard Susskind's Quantum Mechanics: The Theoretical Minimum, he describes a computer program that could fool you into thinking there is a quantum spin in a magnetic field. This spin is inside a ...
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66 views

is decoherence continuous?

Pardon my naivete here. In a quantum system, it seems that even a few photons from the environment can decohere the entangled particles in the system in a trillion trillionth of a second ( or faster). ...
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72 views

Quantum Wavefunctions Without Space

A handful of physicists have a rather peculiar definition of 'nothing' in terms of cosmology. Their claim is that the Universe, assuming it has 0 total energy, could have arisen from nothing but ...
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25 views

What property of medium is directly related to light propagation speed in that medium? [duplicate]

Refractive index is used to calculate phase velocity of light in medium, other than vacuum. Recently I had a discussion with somebody claiming that light is slower due to magnetic field of atoms. I ...
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30 views

Density matrix of a single qubit as a function of its Stokes Parameters

$\newcommand{\bra}[1]{\left\langle#1\right|} \newcommand{\ket}[1]{\left|#1\right\rangle} \newcommand{\prom}[1]{\langle{#1}\rangle} \newcommand{\matrixel}[3]{\bra{#1}{#2}\ket{#3}}$ How can I prove ...
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26 views

Electron interference and light interference

In the double slit experiment I see that shooting electrons one by one after long time create a pattern that resembles that of light interference, but before these long time I see electrons at ...
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100 views

Can you stop an electron in vacuum?

If we shoot an electron in vacuum tube, then stop it with electromagnetic field, and switch off the field, what will happen with electron? Will it continue its movement? If there is a gravitational ...
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117 views

How was it proven that a quantum entanglement measurement of particle A, affects properties of particle B

If I understood the wikipedia article correctly, quantum entanglement claims that information travels instantly between entangled particles. An act of measurement on one of the entangled particles ...
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62 views

Wave Function Collapse Versus Decoherence

I'm aware that wave function collapse is still a topic of debate-and that decoherence is a pretty good explanation for how things might approach wave function collapse, in some sense. But the way I've ...
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91 views

Will Quantum Computation fail if spacetime is discrete?

Will Quantum Computation fail if spacetime is discrete? Basically, would a discrete spacetime impose unexpected limits on how many Qubits could be used in calculations? Conversely, can quantum ...
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46 views

Can the vacuum energy be made finite with quantized space

From what I know the reason we have infinite vacuum energy is because according to Quantum Field Theory at every point in space we something analogous to a harmonic oscillator but since the Zero Point ...
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47 views

Projection operators in a direct product space

The things I'm pretty sure I understand: Let's say I have a single particle hamiltonian $H$ represented by a $2$x$2$ matrix, so it has two eigenstates $|\lambda_1\rangle$ and $|\lambda_2\rangle$. I ...
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75 views

A test for virtual particles by measuring gravity fluctuations possible?

Ok to begin I will begin by talking briefly about my discussions with my Quantum Mechanics (specializes in Particle physics) professor and my Cosmology Professor (who studies particle physics with ...
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84 views

Physical interpretation of a certain Hamiltonian

Consider a $2 \times 2$ Hermitian (or symmetric) matrix-valued function $$g(x) = \{ g_{jk}(x)\}_{j,k=1,2}, \quad x \in \mathbb{R}^{2},$$ such that $0 < m_{-}I \leq g(x) \leq m_{+}I$, for some ...
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48 views

Does every interaction of quantum objects introduce backaction?

The motivation of this question is the following experiment: Assume you have quantum mechanical oscillator, e.g. a particle in a potential $V(q_x)\propto q_x^2$. Now the position of the particle ...
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2k views

Why do we need infinite-dimensional Hilbert spaces in physics?

I am looking for a simple way to understand why do we need infinite-dimensional Hilbert spaces in physics, and when exactly do they become neccessary: in classical, quantum, or relativistic quantum ...
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How did Rutherford's gold foil disprove the plum pudding model?

What stops one of the two following scenarios from happening, consistent with the plum pudding model? The $\alpha$ particle, attracted by the electrons on the outer shell of the pudding, orbits ...
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Does the mass of an electron change with its “energy state”?

When an electron absorbs a photon, it gets into a higher energy state and goes into the upper orbit/shell. Does (rather should) this absorption of energy also have an impact on its mass (although ...
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54 views

Gradient of two-particle system

I'm working on problem 5.1a from Griffiths Intro to QM and given that: $$\mathbf R \equiv \frac{m_1\mathbf{r_1} + m_2 \bf r_2}{m_1+m_2}$$ and $\bf r \equiv \bf r_1 - \bf r_2$ I need to show that, ...
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53 views

What is the relation between renormalization and self-adjoint extension?

What is the relation between renormalization and self-adjoint extension? It seems that a renormalization scheme can be rigorously treated mathematically using the self-adjoint extension theory. Is ...
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56 views

Calculating probability of finding the particle using Dirac notation

An electron can be in one of two potential wells that are so close that it can ‘tunnel’ from one to the other. Its state vector can be written $|ψ\rangle = a|A\rangle + b|B\rangle$, where ...
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920 views

Must Matter Particles Have A Hard Edge?

It's my understanding that electrons are particles, and it's also my understanding that their location while orbiting an atom cannot be determined precisely and must be determined by statistics and ...
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42 views

Frustrated Heisenberg XXZ Model

At the moment, I am look at the frustrated XXZ Heisenberg model, given by the Hamiltonian \begin{align} H=\sum_{i=1}^N\left(J_1S_i^Z S_{i+1}^Z+J_1'\frac{1}{2}(S_i^+S_{i+1}^-+S_i^-S_{i+1}^+)+J_2S_i^Z ...
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47 views

References on De Broglie-Bohm pilot wave theory

Are there any good books related to the not much popular De Broglie-Bohm pilot wave theory and its application in hydrodynamics, walking droplets concepts?
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25 views

Using tracking detector in a double slit experiment, what would we see?

Let's say we put tracking detector (eg. a cloud chamber or a more advanced device) behind the double slits. What would we see? I think the interference pattern is three dimensional. So there are ...
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28 views

Addition of angular momenta, coefficient in the |10> state

In Griffith's text, they apply the lowering operator on the |$11\rangle$ state to get the |$10\rangle$ state. They show this result in two forms on pg. 185: $S_{-}\left(\uparrow\uparrow\right) = ...
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61 views

Why do we care about compatible observables?

Going through my first treatment of quantum mechanics at the Griffiths level, and I was wondering why we care about observables being compatible and what is the significance of having an eigenstate ...
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29 views

Hamiltonian for electron hole

I found in lectures notes that the Hamiltonian containing the energy of a electron hole without any interaction is given by $$H = \sum_k d_k^{\dagger} d_k \left( \frac{\hbar k^2}{2m_V} - E_{0,V} ...
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54 views

How does “observation” affect physics?

I watched this video which very very comprehensively demonstrates concept that sometimes particles behave differently based on whether or not they're being observed. The idea that observing something ...
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Bloch's theorem for Semi-Infinite Lattice

If we have a lattice Hamiltonian $$ \sum_{n'\in\mathbb{Z}}H_{n,n'}\psi_{n'} = E\psi_{n} \,\forall n\in\mathbb{Z} $$ such that $ H_{n,n'} = H_{n+q,n'+q}$ for some $q\in\mathbb{N}$ and for all ...
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50 views

How is $\langle \psi |\psi \rangle$ meaningful in Dirac notation?

I'm reading Quantum Mechanics - A Modern Development, and it explains bra-ket notation, if I understand it correctly, as follows. Let $V$ be a vector space, and let $F$ be a linear function mapping ...
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128 views

Stimulated emission direction

Place a sub-micron clump of crystal violet molecules in front of a multipixel detector. Raise the molecules to an electronically excited state with a beam of 590 nm light, illuminating from the side ...
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90 views

Question about the no-clone theorem

The quantum no-clone theorem states that one cannot "build" a perfect cloning device for arbitrary quantum systems. There also exists a famous thought experiment where Alice transmits information to ...
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Two state Hubbard modell

I am given the two state Hamiltonian $$ H = U \sum_{j \in \{L,R\}} n_{j \uparrow}n_{j \downarrow} - t \sum_{\sigma \in \{\uparrow,\downarrow\}}(a_{L \sigma}^{\dagger}a_{R \sigma} +a_{R ...
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25 views

Strange definition of a two-level system by the Bloch vector

A two-level system can be described by a density operator involving the Bloch vector $$ \vec{r}; \quad r_x = Tr(\rho X); \quad r_y = Tr(\rho Y); \quad r_z = Tr(\rho Z) $$ as $$ \rho = \frac{I + ...
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96 views

Eigenstates of Spin

Why are the eigenstates of spin vectors and not functions? Is this because the spin, $s$, and magnetic quantum number, $m$, take discrete values? My textbook in an earlier section used $Y_\ell ^m$ as ...
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51 views

Why is the ground state energy of the Heisenberg XXZ Model unbounded for some values of $J$?

At the moment, I'm looking at numerically studying the Heisenberg XXZ model. The Hamiltonian is given below: $$ H=\sum_{j=1}^{N-1}\left(J S_j^z ...
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1answer
82 views

Least Action Principle (Classical and Quantum Theory)

I) My first question would be "why should classical systems obey the principle of least action ?" When we find out the propagator in quantum physics, we find the amplitude to be equal to the sum over ...
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48 views

Estimate of the second shallowest bound state?

Suppose we have a 1D potential $V(x)$ of finite range, i.e., $$ V(x) ~=~0 $$ for $|x| > b $. The potential is assume to support at least two bound states, but might have more, say $n\geq 2$. ...
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16 views

Is uncertainty in velocity via HUP reference frame dependent? [duplicate]

Simply put HUP involves position and momentum, further more consider a mass of 1kg. as momentum is mass X velocity = 1X velocity = velocity for calculation purposes. now for a stationary observer the ...
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94 views

References for experimental results of the double-slit experiment

Every other popular science book and intro level text on QM starts with the double slit experiment. It is always just stated as a fact that experiments have been done, actual data is never presented ...
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What is a good book describing the major experiments in Quantum mechanics? [closed]

I need some book suggestions on few of the major experiments done in Quantum Mechanics which are important in terms of what they imply, how they prove or disprove any theory that still exists or was ...
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255 views

How to know if a wave function is physically acceptable solution of a Schrödinger equation?

How does one decide whether a wave function is a physically acceptable solution of the Schrödinger equation? For example: $\tan x$ , $\sin x$, $1/x$, and so on.