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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How to derive or justify the expressions of momentum operator and energy operator?

It has been noted here$\! { \, }^{\text(1, 2)}$, for instance, that $$\mathbf{F} = \frac{d}{dt}\!\!\biggl[ \, \mathbf{p} \, \biggr]$$ is true in all contexts. Likewise, in notable contexts it is ...
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66 views

In what range the acceleration value of quantum particle lies?

According to Heisenberg's uncertainity principle, the position and velocity of an quantum particle cannot be determined simultaneously. Is it possible to determine position and acceleration ...
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1k views

Expectation value of total energy for the quantum harmonic oscillator [closed]

A particles unnormalized wavefunction is given as $$\psi(x)=2\psi_1+\psi_2+2\psi_3.$$ How can I find $\langle E\rangle $ without calculating $\langle T\rangle$ or $\langle V\rangle $ ...
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190 views

The irreducible observer

This question probably verges on pseudo-science and probably sounds like gibberish, so please pardon me. But I'll ask it anyway. In an ideal lab experiment there is generally a separation between the ...
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250 views

On the atomic level, how is incandescent light structured?

I want to know from the smallest possible originating structures how the light I see generated from heat is made by atoms themselves.
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218 views

Should normalisation factor in a QM always be positive?

I have a fairly simple question about a normalisation factor. After normalising a wavefunction for a particle in an infinite square well on an interval $-L/2<x<L/2$ I got a quadratic equation ...
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531 views

Do electrons have a radius when they behave like a particle?

I know sometimes electrons behave like waves, but it sometimes can be seen as a particle. while it's a particle, does it have a radius? or, a volume? If it doesn't even have a volume, how can we still ...
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50 views

What is the volume of electron? [duplicate]

I know that electron has mass , and that is particle( a body which has only mass and whose size is negligible) but can we ever calculate the volume of the electron . if yes how much it is . if no why? ...
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196 views

Wave equations for two intervals at Potential step

Lets say we have a potential step as in the picture: In the region I there is a free particle with a wavefunction $\psi_I$ while in the region II the wave function will be $\psi_{II}$. Let me ...
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5k views

Product of exponential of operators

in the context of non-relativistic quantum mechanics I want to show that, for any $A$ and $B$ operators $$e^{A}e^{B}=e^{A+B} $$ if and only if $$[A,B]=0$$ I remember my professor told use about ...
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637 views

Fourier transform between $x$ and $p$

On this page right at the top they mention two sets of fourier transform. First set is connection between $x$ (position) and $k$ (wave vector) space: $$ \begin{split} f(x) &= ...
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3answers
473 views

Why is $\int (dp/2\pi) |p \rangle\langle p| = 1 $?

In quantum mechanics, why is $\int (dp/2\pi) |p \rangle\langle p| = 1 $ where $|p \rangle$ represents momentum eigenstate?
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Can experiment distinguish the basis in which a singlet state is represented?

Let $\left(|\uparrow\rangle,|\downarrow\rangle\right)$ and $\left(|\nearrow\rangle,|\swarrow\rangle\right)$ be two bases of the $2$-dimensional Hilbert space $H$. Can an experiment distinguish ...
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177 views

What would be the requirement to learn matrix mechanics? [duplicate]

What would be the requirement to learn matrix mechanics? More specifically, what math do I need? Can anyone recommend me a book that covers all maths needed for matrix mechanics?
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142 views

Can we develop in the future a technology that can send a message to the past? [duplicate]

Possible Duplicate: Is it possible to go back in time? I believe that everything is possible in this world. If that can be done then why aren't we receiving any message from the future.
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121 views

Difference between $|0\rangle$ and $0$ in the context of isospin

I know this has been asked before, but I am confused having read it in the context of isospin, where the creation operators act on the "vacuum" state (representing no particles) $$a^\dagger_m|0\rangle ...
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1answer
396 views

Two-state system problem

Given a 2-state system with (complete set) orthonormal eigenstates $u_1, u_2$ with eigenvalues $E_1, E_2$ respectively, where $E_2>E_1$, and there exists a linear operator $\hat{L}$ with ...
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Can quantum communication really replace electromagnetic waves for telecommunication medium in future?

Currently I am planning to get masters degree. So I am thinking about a subject in which I have to get masters degree. Following are my questions to leading physicists.. Which technology is the ...
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82 views

How to derive Uncertainty Principle relation?

How to derive Heisenberg Uncertainty Principle relation?
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51 views

Applying Schrodinger equation to find the energies of a free electron model in a metal [closed]

The one-particle Hamiltonian is given by $$\hat{H}=\frac{1}{2m}\left(p+\frac{e}{c}A\right)$$ with $e > 0$ and vector potential $A=(0,x,0)B$, such $B=\triangledown \times A=(0,0,B)$ Question: "I ...
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1answer
72 views

Two site Hamiltonian [closed]

So my question is I have this Hamiltonian: $$ H = \sum_i \epsilon_i \sigma^+_i\sigma^-_i + \sum_{i\neq j} V_{ij} \sigma^+_i \sigma^-_j, $$ and I want to write it out for two site. Is this correct?: ...
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1answer
111 views

Field quanta- infinite in extent? [duplicate]

Possible Duplicate: confusion on quantum field theory Are field quanta infinite in extent as stated in Art Hobsons paper? What does this even mean? I've not seen any electrons or atoms that ...
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3answers
3k views

The Double Slit Experiment and the changing of electron behaviour

As you will all know, when one tries to detect which slit an electron has gone through with close up observation, it changes from behaving like a wave and producing an interference pattern to behaving ...
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2answers
208 views

Show that the energy levels of a particle in a specific potential are $E_n=(n+\frac{1}{2})h\omega-\frac{1}{2}\frac{F^2}{m\omega^2}$ [closed]

A particle of mass m moves on the x-axis under the influence of the potential $$V(x)=\frac{1}{2}m\omega^2x^2+Fx$$ Can anyone help me, using Schrödinger's equation in one dimension that the energy ...
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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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101 views

Linearity in Quantum Mechanics that make superposition possible

As a beginner in QM, all the video lectures that i have seen talk about superposing wave functions in order to get $\psi$. But from what i know from linear algebra, the system must be linear in order ...
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1answer
115 views

probability amplitude and path integrals [closed]

Recently, I have been learning about path integrals and I was wondering, can the probability of a certain path be weighted more in a path integral? Said in another way, can certain paths have more ...
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1answer
221 views

Collapse in Quantum Field Theory? [duplicate]

I do not want answers telling me that wave-function collapse is not real and decoherence is the answer (I know the situation with that). I am asking a question purely on the basis if wave-function ...
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What really is the smallest “mass” or “object” in the universe?

Look at this here. With respect to the sciences, the atom is obviously not the smallest piece of mass. Apparently, if people have already broken down the atom in to particles smaller than so, why ...
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146 views

Proving (instead of discovering) the laws of quantum mechanics

A single toss of a fair coin cannot be predicted. But if we observe a large number of tosses, we can prove mathematically the law that roughly half of them will show up heads. The movements of ...