# Questions tagged [quantum-mechanics]

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 quantum-field-theory tag for the theory of many-body quantum-mechanical systems.

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### Why do we call $x$ a constant while mentioning eigenfunctions of the position operator?

For a position eigenstate $\psi_x$, we say $$\hat{x}\psi_x=x\psi_x$$ Since it's an eigenfunction, we say that the result of using the operator is "a constant times the function itself". But $x$ isn't ...
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### 3D harmonic oscillator magic numbers

I know that, $$V(r) = (1/2) m \omega^2 r^2 ,$$ $$\omega \approx 40(Z+N)^{-1/3}\ \rm{MeV}$$ and $$E = (n+3/2) \hbar \omega.$$ How do you find the magic numbers of protons and neutrons which ...
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### Has anyone tried to incorporate other forces in GR-like theory rather than incorporate gravity in QM? [duplicate]

Has anyone tried to imagine other three forces in a way similar to gravity, i.e., warping some higher dimensions of spacetime to create a curvature. If there is such a theory, where does it fail?
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### Differentiation of a ket vector with respect to a spatial dimension

Consider a state $|\psi\rangle$. While discussing the Schroedinger equation, we say $$\hat{H}|\Psi(t)\rangle=i\hbar\frac{\partial}{\partial t}|\Psi(t)\rangle$$ We also define the hamiltonian operator ...
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### Simple way to modify the diagonal elements of the hamiltonian after adding a strong interaction

Let's say we have a hamiltonian of a non-interactive system of two particles. We have correctly worked out the matrix form of the hamiltonian. Now, if we add a very strong attractive interaction ...
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### Single-particle Green's function

Define a single-particle Green's function as $$i\hbar G(xt;x't') = \langle x| e^{-iH(t-t')/\hbar} | x'\rangle.$$ By inserting the completeness relation, we have \begin{...
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### Determining the state of a system

My textbook says: "To determine the state of a system at a given instant, it suffices to perform on the system a set of measurements corresponding to a complete set of commuting observables (CSCO)" ...
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### Relation between Wigner flows and entropy

After reading this question What's the intuitive reason that phase space flow is incompressible in Classical Mechanics but compressible in Quantum Mechanics? and some papers of Steuernagel’s group,...
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### Solutions that are part of the Hilbert space

Why do we omit solutions that do not converge at $\pm\infty$ from the physical Hilbert space, what is the argument for us being allowed to do so?
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### Question about the “wave function” on Relativistic Quantum Mechanics (RQM) and Quantum Field Theory (QFT)

I'm enrolled on a short and conceptual couse on RQM and QFT and the professor made a distinction about the Klein-Gordon (K-G) equation on RQM and the K-G equation on QFT. Roughly speaking, he said ...
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### Why can't quantum field theory be complex instead of imaginary?

In the following question 1, the author claims that a QFT is defined as: $$Z[J] \propto \int e^{iS[\phi]+J.\phi} D[\phi]$$ Then uses this definition to explore the possibility of formulating a QFT ...
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### Does the static gravitational field move with the source instantly?

I have read this question: How fast does gravity propagate? where hawkeye says: So what does that mean? It means that the "speed of gravity" is the speed of light … technically. Changes in ...
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### Heisenberg uncertainty principle in daily life

I need some examples of the Heisenberg uncertainty principle on a basic level, or if possible in daily life. Or maybe a simple explanation for validity of the principle in easier words. I cannot get ...
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### Is the Quantum Zeno Effect real? [duplicate]

When a decaying particle is observed using the Quantum Zeno Effect, can the decay of this particle be delayed or prevented?
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### Derivation of the Guiding Wave equation

I've been searching around the internet for a derivation of the guiding wave equation, but I can't find a derivation anywhere. I know that Bohmian Mechanics is not a mainstream idea but I was hoping ...
Referring to the Hamiltonian of a system of free electrons, $$H_0= \sum_{\sigma} \int d^3rd^3r' \psi_{\sigma}^{\dagger}(\mathbf{r})\left(- \frac{\hbar^2}{2m}\nabla^2\right)\delta(\mathbf{r}-\mathbf{... 0answers 36 views ### If time is always passing, at what increment/speed is it passing in? [duplicate] If time is always unfolding around us it must be occurring in some increment or speed, if answerable, what speed or increment would time be moving in? If not answerable, would there be a way to figure ... 3answers 77 views ### Negative energy in bound states of a particle in a finite potential well Consider you have a particle in a finite potential well as depicted in the photo attached. Now we have three regions:$$V(x) = \begin{cases} 0, & \text{for } x<-a & (1)\\ -V_0, & \...
In Peskin & Schröder QFT, just before equation 7.93, he writes in passing, Next let us examine how $\Pi _2 (q^2)$ modifies the electromagnetic interaction, as determined by Eq. (7.77). In the ...