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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Why is the contribution of a path in Feynmans path integral formalism $\sim e^{(i/\hbar)S[x(t)]}$

In Feynman's book "Quantum Mechanics and Path Integrals" Feynman states that the probability $P(b,a)$ to go from point $x_a$ at time $t_a$ to the point $x_b$ at the time $t_b$ is $P(b,a) = ...
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2answers
398 views

Is energy exchange quantized?

In the photoelectric effect there is a threshold frequency that must be exceeded, to observe any electron emission, I have two questions about this. I) Lower than threshold: What happen with lesser ...
12
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4answers
886 views

How do I correctly interpret $\rho = \psi_1^* \psi_2$?

Summary: This turned out to be a rather trivial one indeed. As Marek mentioned in the comment, the continuity equation is trivial. And it indeed turns out be so. Godfrey Miller elaborates on this, ...
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1answer
701 views

Open shells in Quantum mechanics of multielectron atoms

This question: How do electron configuration microstates map to term symbols? And the discussion of multielectron effects here: Quantum Computing and Animal Navigation Inspired me to try to understand ...
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3answers
399 views

What is the difference between $|0\rangle $ and $0$?

What is the difference between $|0\rangle $ and $0$ in the context of $$a_- |0\rangle =0~?$$
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How do electron configuration microstates map to term symbols?

I am trying to understand energy levels of electron configurations. I visited the NIST web site and discovered that the notation used here are called term symbols. After reading corresponding ...
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2answers
1k views

How to measure the spin of a neutral particle?

If a charged particle with charge $q$ and mass $m$ has spin $s \neq 0$ we can measure an intrinsic magnetic moment $\mu = g \frac{q}{2m}\hbar \sqrt{s(s+1)}$. This is how spin was discovered in the ...
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1answer
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Scale set by cosmological constant

Following on Jim Graber's answer to: Can "big rip" rip apart an atomic nucleus? If the cosmological constant is large enough, even the ground state of a hydrogen atom can be affected. So ...
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3answers
344 views

Is it possible to bind an entangled electron to the outer shell of an atom or just a proton?

Say we start with an entangled electron--positron pair and we separate them. I want to take the entangled electron and bind it to a proton or the outer shell of an atom. Is it possible to do this ...
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1answer
207 views

Is the quantum state or information of a particle is all that differentiates it from another particle?

So I have learned in my QM classes that you can't tell one electron from another electron. They are indistinguishable. I also learned that the wavefunction of a particle includes the spacial part and ...
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3answers
2k views

Why electrons behave as a particle and also as a wave?

Why do electrons (and other very small particles) sometimes behave as particles (i.e. when we are not looking at them) where as other times they behave as waves?
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4answers
222 views

What are the conditions to be satisfied by a theory in order to be a quantum theory?

This is in continuation to my previous question. It is not a duplicate of the previous one. This question arises because of the answers and discussions in that question. Can we call a theory, quantum ...
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414 views

Are the basic postulates of QM the only set of postulates that can give rise to a sensible semi-probabilistic physical theory?

Are the basic postulates of QM, such as complex Hilbert space, unitary evolution, Hermitian operator observables, projection hypothesis etc., the unique and only set of postulates that gives rise to a ...
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6answers
309 views

Does the HUP alone ensure the randomness in QT?

This answer of mine has been strongly criticized on the ground that it is no more than a philosophical blabbering. Well, it may well be. But people seem to be of the opinion that HUP alone does not ...
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2answers
2k views

Einstein's box - unclear about Bohr's retort

I was reading a book on the history of Quantum Mechanics and I got intrigued by the gendankenexperiment proposed by Einstein to Bohr at the 6th Solvay conference in 1930. For context, the thought ...
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1answer
454 views

Measuring the magnitude of the magnetic field of a single electron due to its spin

Is it possible to measure the magnitude of the magnetic field of a single electron due to its spin? The electron's intrinsic magnetic field is not dependent upon the amount of energy it has does it? ...
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3answers
268 views

Knowing when wavefunction collapses

So I learned that after a measurement of, lets say the position of the wavefunction of a particle is made, if another measurement of the position of the particle is made right away, you should get the ...
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3answers
1k views

Is “analog” quantum-computation not useful?

I understand what a qubit-based quantum computer by the current definition is and how they are constructed. I read another thread where someone suggested encoding a computation into a dual-slit ...
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7answers
4k views

Eigenvalues of an operator correspond to energy states in quantum mechanics, why?

When finding the discrete energy states of a operator I have been taught to use the time-independent Schrodinger equation which restates the definition of eigenvalues and eigenvectors. What I don’t ...
11
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1answer
4k views

Phase shifts in scattering theory

I have been studying scattering theory in Sakurai's quantum mechanics. The phase shift in scattering theory has been a major conceptual and computational stumbling block for me. How (if at all) does ...
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2answers
354 views

Distinguishability in Quantum Ensembles

Inspired by this question: Are these two quantum systems distinguishable? and discussion therein. Given an ensemble of states, the randomness of a measurement outcome can be due to classical reasons ...
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10answers
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About the complex nature of the wave function?

1. Why is the wave function complex? I've collected some layman explanations but they are incomplete and unsatisfactory. However in the book by Merzbacher in the initial few pages he provides an ...
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7answers
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Are these two quantum systems distinguishable?

Suppose Stanford Research Systems starts selling a two-level atom factory. Your grad student pushes a button, and bang, he gets a two level atom. Half the time the atom is produced in the ground ...
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3answers
1k views

How to tell if QM is really random?

Given a stream of random binary numbers(*) Is there any way to differentiate if they came from a Truly Random or from a formula/algorithm ? how? if there is no way to decide this, then, I can't find ...
3
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2answers
538 views

Observing the exponential growth of Hilbert space?

One of the weirdest things about quantum mechanics (QM) is the exponential growth of the dimensions of Hilbert space with increasing number of particles. This was already discussed by Born and ...
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3answers
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Photon hitting an atom with higher energy than needed to ionize

Suppose we have an atom with several energy levels (e.g. an hydrogen), and it is hit by photons. I know that in order to have the atom change energy levels, the photon must have an energy level ...
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5answers
253 views

Does quantum mechanics allow us to formulate causally sufficient conditions for the occurrence of an outcome?

This is a follow-up question to "In QM, why do the probabilities ... add up to 1?". No actual measurement is perfect. While theorists may ignore this, experimenters know well enough that in many runs ...
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6answers
731 views

In quantum mechanics, why do the probabilities of the possible outcomes of a measurement add up to 1?

The question assumes the standard formalism with projector-valued measures rather than POVMs. Suppose a measurement has two possible outcomes, and the corresponding probabilities are greater than 0 ...
5
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2answers
416 views

What happens when particle-antiparticle pairs annihilate in MWI?

The many-worlds interpretation of quantum physics is built around a configuration space, where the position of a particle is three components of the position of that universe. What happens with ...
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7answers
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Why is a classical formalism necessary for quantum mechanics?

This is not a question pertaining to interpretations, after the last one I realized I should not open Pandora's Box ;) For theories to be consistent, they must reduced to known laws in the classical ...
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1answer
468 views

What's the relevance of Efimov physics?

Is it something unexpected?Why universality in cold atomic gases is important?What researches are looking for?Can this be useful for topological quantum computers? Can we expect a whole myriad of ...
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1answer
376 views

Does quantum mechanics prohibit extraterrestrial life? [closed]

There is a known thought experiment, connected to quantum immortality: a duel between physicist and a philosopher. Each turn physicist and philosopher fire at each other with a pistol. The quantum ...
9
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2answers
2k views

Perturbation theory with degeneracy even after 1st order

Most textbooks on basic quantum mechanics tell you that when your initial Hamiltonian $H_0$ has degenerate states, then before you can do (time independent) perturbation theory with a perturbation ...
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1answer
668 views

Proving Operator identities (Quantum Physics)

How would I go about showing: $$\hat{A}^{\dagger} + \hat{B}^{\dagger} = \left( \hat{A} + \hat{B} \right) ^{\dagger}$$
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2answers
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What is in the space between a nucleus of an atom and its electrons?

There is a common analogy about the structure of an atom, such as the nucleus is a fly in the centre of a sports stadium and the electrons are tiny tiny gnats circling the stadium (tip of the hat to ...
7
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1answer
632 views

Question about a Limit of Gaussian Integrals and how it relates to Path Integration (if at all)?

I have come across a limit of Gaussian integrals in the literature and am wondering if this is a well known result. The background for this problem comes from the composition of Brownian motion and ...
5
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1answer
660 views

The Heisenberg limit is not a limit?

This new Best-ever quantum measurement breaks Heisenberg limit PHYSICISTS have made the most accurate quantum measurement yet, breaking a theoretical limit named for Werner Heisenberg. ...
15
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6answers
3k views

Disproof of Bell’s Theorem

The half-page arxiv doc by Joy Christian of Oxford Uni, UK has the Title and Abstract: Disproof of Bell’s Theorem We illustrate an explicit counterexample to Bell’s theorem by constructing a ...
6
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4answers
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Chemical potential

This is something probably very basic but I was led back to this issue while listening to a recent seminar by Allan Adams on holographic superconductors. He seemed very worried to have a theory at ...
7
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1answer
774 views

Recent breakthroughs in quantum computing?

Can anyone explain to me why we have had no major breakthroughs in the theory of quantum computation in the past 15 years? Shor's algorithm set the standard, since then we've had Grover's algorithm ...
2
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3answers
713 views

Causality and Quantum uncertainty [duplicate]

Possible Duplicates: Why quantum entanglement is considered to be active link between particles? Why can't the outcome of a QM measurement be calculated a-priori? Why do some (the majority ...
6
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3answers
301 views

References on the non-compositeness of the known elementary particles

What paper(s) or theory(s) describe or prove that the elementary particles that we have determined today cannot be made up of smaller more fundamental particles?
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1answer
487 views

Canonical momentum operators in curvilinear coordinates

What is the quantum canonical momentum operator corresponding to arbitrary canonical position. For example, in Cartesian coordinates ($x^i$), the canonical momentum operator with respect to each $x^i$ ...
3
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3answers
173 views

Are there measurable effects to scaling the action by a constant?

Classically, we obtain the equations of motion by finding a path which has an action that is stationary with respect to small changes in the path. That is the path for which: $\delta S =0$ Scaling ...
4
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3answers
761 views

Is contextuality required in quantum mechanics?

I still don't really understand what contextuality means in reference to quantum mechanics. If someone could give a clear definition that would be great. It sounds like it means you can't always ...
14
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5answers
1k views

What combinations of realism, non-locality, and contextuality are ruled out in quantum theory?

Bell's inequality theorem, along with experimental evidence, shows that we cannot have both realism and locality. While I don't fully understand it, Leggett's inequality takes this a step further and ...
3
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1answer
162 views

What are the statistics of three to five bosons?

This should be a very easy question. If you look at the bottom of "Identical Particles" in Wikipedia, you see Table 1, which gives you the two particle statistics for bosons, fermions and ...
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5answers
2k views

Does Heisenberg's uncertainty under time evolution always grow?

Recently there have been some interesting questions on standard QM and especially on uncertainty principle and I enjoyed reviewing these basic concepts. And I came to realize I have an interesting ...
3
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2answers
294 views

Web references for Nelson's “Quantum Fluctuations”?

Edward Nelson's book "Quantum Fluctuations" (Princeton UP, 1985) gives an alternative way to introduce trajectories, quite different to the trajectories of de Broglie-Bohm type approaches. I've read ...
4
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3answers
429 views

Young's experiment or why the light can't be described as a particle [closed]

Who hasn't heard about the double-slit experiment? It figures in any book of quantum physics. But there is something no one can explain to me : I understand why the light cannot be described only as a ...