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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Do the same experiments yield different results due to the principle of uncertainty?

When thinking about small particles and their uncertainity, I've allways rather seen them being all over the place rather than randomly changing location. I would think that, in the same time, you'd ...
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68 views

Does quantum entanglement imply the existence of a non-causal structure connecting space-time together?

In contrast to a "time-like" or "causal" structure connecting space-time together, Does quantum entanglement imply the existence of a "space-like" or "non-causal" structure holding space-time together ...
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1answer
82 views

What would happen if two entangled particles collided?

Does that is even possible? I have almost zero knowledge in quantum physics, it is just a curiosity that popped in my mind.
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14 views

Weak measurement formalism: Weak value can be too big?

A question to experts in the weak measurement formalism: In the famous paper How the Result of a Measurement of a Component of the Spin of a Spin-1/2 Particle Can Turn Out to be 100 by Aharonov, ...
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57 views

Calculating Quantum number from initial conditions

I have solved the particle in a box problem to get energy eigenstates and wave vectors: $$E_{n}=\frac{\hbar^{2} k^2}{2m} ,\hspace{1cm} k_{n}=\frac{\pi n}{L}$$ And now I am trying to figure out how ...
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70 views

Inner product of position and momentum eigenkets

Let's define $\hat{q},\ \hat{p}$ the positon and momentum quantum operators, $\hat{a}$ the annihilation operator and $\hat{a}_1,\ \hat{a}_2$ with its real and imaginary part, such that $$ \hat{a} = ...
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57 views

Proof involving the fine-structure Hamiltonian of the Hydrogen atom

Given the perturbed Hamiltonian of the Hydrogen atom: $$ ...
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1answer
65 views

Blackbody and standing waves

I'm reading articles about black body radiation and why classical mechanics fails to explain it. My question is: Why do EM waves have to be standing wave in a cavity?
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12 views

Modelling of nuclear motions (Classification) after invoking the BO approximation

I know that after invoking the Born-Oppenheimer approximation, the nuclei will move on the adiabatic potential provided by the electronic energy (also called potential energy surface (PES)). Such ...
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44 views

Do restrictions on quantum mechanical measurement always just work out to avoid contradictions?

Classically it was said that measurement leads to a collapse of the wave function. However, if there wouldn't be any limit on the process on measurement itself, strange things can happen, e.g. a ...
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45 views

Quantum Fourier Transform question regarding measurement

When we use the quantum fourier transform, for a function, the output is entangled, so if a measurement is made on the output, the result may not be that of the function that one wanted in the first ...
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2answers
95 views

Bloch Sphere and $SU(2) \to SO(3)$ map

For any matrix $U \in SU(2)$ there is an associated map from $S^2$ (the surface of a 3-disk) to itself defined by $\pi \circ U$, where $\pi$ is the projection map from $\mathbb{C}^2$ to $CP(1)$, that ...
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21 views

Magnetic moment with external magnetic field on a lattice?

Consider a system in which atoms are located in a regular lattice, each atom having a spin $1/2$ and an associated intrinsic magnetic moment $\mu_0>0$. Assume that each atom interacts only weakly ...
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2answers
44 views

Energy of an EM Wave and its temperature and amplitude

I'm trying to understand why classical physics fails to explain black body radiation. I'm confused. According to Boltzmann, energy calculation for em wave is based on temperature. According to ...
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1answer
84 views

Contribution to angular momentum $ L_z$ - due to rotation of probability fluid?

I'm doing a course on QM and this concept is entirely new to me: "The eigenvalue $m\hbar$ of $L_z$ can be understood as the result from the rotational motion of probability fluid around the z-axis. " ...
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32 views

Experimental proof of the principle of superposition in QM [duplicate]

I have read that we need all operators in QM to be linear to confirm the principle of superposition which is experimentally well proven. I wonder how such an experiment could be made?
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27 views

Quantum Fourier Transform question

We can formulate a Quantum Fourier Transfrom which is derived from a DFT. This DFT performs a polynomial operation by interpolating over specific sample points, and then when we read the output from ...
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28 views

I would like to ask any interested reader about “Quantum Bidding in Bridge”

see http://journals.aps.org/prx/pdf/10.1103/PhysRevX.4.021047 I would like to see how specific examples are worked out. Specifically, details on how the quantum protocol in figure 1. of the above ...
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1answer
27 views

Nodes in wave functions outside of the classical turning point

When looking at the solutions of the classical harmonic oscillator for instance from wikipedia one can observe that there are no nodes in the wavefunction outside the classical turning points. But I ...
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60 views

Calculation of energy eigenvalues of $\hat{x}^4$

I would appreciate help in calculating the energy eigenvalues associated with $\hat{x}^4$, with $\hat{x}$ expressed using the ladder operators for harmonic oscillators. $\hat{x} = ...
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6 views

Condensate fraction and momentum distribution in cold atom experiments

In ultrcold atom experiments, people usually use time-of-flight technique to measure the momentum distribution, then get the condensate fraction information from the interference pattern. What is the ...
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3answers
145 views

Wavefunction collapse to a state that seems impossible

Let $\Omega$ be an observable and let $\Psi = \sum a_i\phi_i$ be a decomposition of a state of a system (satisfying the Schrödinger equation) in eigenfunctions of $\Omega$ (assume for simplicity it is ...
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1answer
73 views

Significance of an operator with a negative variance

Suppose we have a quantum state, well described by its time-independent wave function $\Psi$. And we have a well-defined Hermitian (self-adjoint) operator $\hat{A}$. We successfully evaluate the ...
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1answer
98 views

What exactly is a coherent state and why is it interesting?

Please note that I do not have a background in physics, so if possible please refrain from a bunch of $ |x\rangle $ notations, unless clearly specifying what it symbolically means. So I have been ...
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35 views

Transition Between Position and Momentum Basis

I'm having some trouble following pages 55-56 of Sakurai's Modern Quantum Mechanics. We're trying to transfer from position space into momentum space. Here's a quote: Let us now establish the ...
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20 views

A question on lowering the total spin

Is there a way to lower the total spin of the state and fixing the $S_z$ rather than lowering the $S_z$ by spin ladder operator? Or in other words, how to connect the $S=1$ state with $S=2$ or $S=0$ ...
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1answer
54 views

Particle in a box: simultaneously bounded momentum and position

While writing an answer to this question, I started doubting about the interpretation of the uncertainty principle for the particle in a box. In the 1-dimensional particle in a box problem, explicit ...
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3answers
88 views

Can one construct a new operator in terms of the powers of another operator?

Suppose we have a quantum state, well described by its time-independent wave function Psi. And we have a well-defined Hermitian (self-adjoint) operator $A$. We successfully evaluate the expectation ...
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1answer
66 views

Trace operation on dynamic equation: physical meaning?

Suppose we have Heisenberg equation of motion for some observable $A$, $$ i\hbar\frac{dA}{dt}= -[H,A] $$ since the trace of any finite dimensional commutator structure vanish(not something like ...
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3answers
98 views

Could this suggest that there is a wavelength smaller than Planck's?

Suppose the earth receives a photon with a wavelength $\gamma_1$. Since spacetime is expanding, we know that this photon had an original wavelength $\gamma_2$, such that $\gamma_2\lt\gamma_1$. This is ...
14
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1answer
848 views

Is the Uncertainty Principle valid for information about the past?

My layman understanding of the Uncertainty Principle is that you can't determine the both the position and momentum of a particle at the same point in time, because measuring one variable changes the ...
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0answers
46 views

Most natural tensor structure for a quantum field

A quantum field is described by a Hilbert space. In many instances, the chosen tensor structure on this Hilbert space corresponds to that of space-like separated regions of space-time. The ...
2
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2answers
35 views

Diffraction of electron through graphite film

"Electrons of wavelength 434 nm are directed into a thin film of graphite. Will they diffract?" Ignoring relativistic effects, I used de Brogile's relation, $p = \frac{h}{\lambda}$, to determine ...
3
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1answer
83 views

What is the motivation for introducing “ontological state” in 't Hooft's deterministic quantum mechanics

I tried to read Prof. 't Hooft's new paper The Cellular Automaton Interpretation of Quantum Mechanics A View on the Quantum Nature of our Universe, Compulsory or Impossible? and encountered difficulty ...
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2answers
64 views

How can $J_1^2, J_2^2, J_{1z}, J_{2z}$ commute mutually?

I'm reading through J. J. Sakurai's Modern Quantum Mechanics book and currently looking at the "Angular-momentum addition" part. Here, it says you have two options and that one option is to ...
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1answer
19 views

Photoelectric effect at low frequencies [duplicate]

Through the photoelectric effect among many others we learn that light is actually comprised of discreet quanta of energy. That's because of the energy of the emitted electrons as well as the minimum ...
2
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0answers
40 views

Proving that Measurement increases von Neumann entropy

Let $V$ be a finite dimensional complex inner product space. Let $\mathcal{M}$ be the classical sample space of measurement outcomes that may occur in a given experiment, and $M_\mu$, $\mu \in ...
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4answers
531 views

Can we say there are 2 EM radiation types?

EM radiation seems to come from two different sources: According to the Maxwell, by acceleration of electrons According to the Bohr, by jumping of electrons between energy levels? Are these two, ...
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1answer
71 views

In quantum mechanics, why position and momentum are related by Fourier Transformation(only)? [duplicate]

We know that if we take Fourier transform of momentum we go to position space. But why Fourier transform only.(credit_ Abh Gupta)
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6answers
158 views

Could this mean that Schrodinger's Cat thought experiment is false?

Since it is uncertain on whether or not the cat could be dead or alive, it is concluded that it depends on the observer to make it either dead or alive. But lets look at a clock. It doesn't take ...
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1answer
90 views

The relation between classical and quantum vacua

First let me clarify what I mean by vacuum. Suppose we are concerned with a theory of fields $\phi ^i$ defined on a stationary globally hyperbolic spacetime $M$ (I want the spacetime to be stationary ...
4
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1answer
118 views

Is this a photograph of an electron-positron annihilation? [closed]

With degrees in Mechanical and Electrical engineering but no advanced education in physics, I submit a query based on ellipsometric macro photography of TEMS supplied by FDA/NIH. In one TEM a ...
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15 views

Ask procedure to obtain reduced density matrix

I have a mutipartite system; the subsysyems having interacted. Now, to find reduced density matrix for any single subsystem, is the order of partial traces(over remaining subsystems) important?
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0answers
19 views

Is there a relation between Fokker-Planck equation and Lindblad equation in open quantum system

Is there a relation between the Fokker-Planck equation and the Lindblad equation, a quantum Markovian master equation in the open quantum system?
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0answers
35 views

Self-adjoint extensions with 'teletransporting' boundary conditions

When choosing a self-adjoint extension of a Hamiltonian, in general one can obtain domains in which (i) the probabilities teleport* between points on the boundary and (ii) boundary conditions ...
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2answers
69 views

Spacetime, space observables and time observables

It appears to me that the concepts of space and time play a privileged role in Physical Theories. If we look at classical non-relativistic theories such as point particle mechanics, rigid body ...
4
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0answers
52 views

Interchange symmetry for states with identical particles

I was reading this web page about interchange symmetry for states with identical particles here: http://quantummechanics.ucsd.edu/ph130a/130_notes/node317.html The article states that the highest ...
11
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4answers
516 views

With redshift, energy is lost. Where does it go? [duplicate]

A photon emitted by a distant source billions of light years away arrives here with a lower frequency hence less energy than it started with. What happened to the energy?
3
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2answers
36 views

Orbital plot to explain bonding and anti-bonding molecular orbitals

Related is this question: Molecular and Atomic Orbitals and Antibonding. In my textbook on organic chemistry they represent an orbital as a 2d wave function to explain the formation of bonding and ...
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21 views

Infinite Round Square-Well zeroes of Spherical Bessel function

Consider a potential well where the potential is zero within a spherical well of radius a centered on the origin. Taking $a$ as our length scale and $\hslash^2/(2ma^2)$ as our energy scale, we gain ...