# Tagged Questions

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### Generalisation of a particle in QFT

In classical mechanics, we assumed a particle to have a definite momentum and a definite position. Afterwards, with Quantum mechanics, we gave up the concept of a time-dependend position and momentum, ...
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### Feynman's derivation of the Schrödinger equation

I'm reading the following article: Feynman's derivation of the SchrÃ¶dinger equation In this article, the autor claims that Feynman derivation of the SchrÃ¶dinger equation was a key aspect of the ...
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### Lack of Maslov index in the path integral formalism

Introduction Consider Feynman's famous path integral formula K(x_a,x_b) = \int \mathcal{D}[x(t)] \exp \left[ \frac{i}{\hbar} \int_{t_a}^{t_b} dt \, \mathcal{L}(x(t),\dot{x}(t),t) \...
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### How to generalize the Bohr-Sommerfeld quantization condition to more dimensions?

As in the title-how to consider this condition on e.g. a polar or spherical coordinate system, with two or three dimensions? Which different methods I can use? EDIT: the coordinate system doesn't ...
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### WKB Approximation on an linear + harmonic potential

I have a quick question: I have performed the WKB approximation to find the energies of bound states in symmetric potentials (Square, harmonic, ...). To do this I just find the "turning points" by ...
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### Why are electrons treated classically in cyclotron measurements?

As I understand , systems having large angular momenta relative to the planck constant (limit of large quantum numbers, e.g. $J/\hbar \to \infty$), can be treated as classical systems. Now in the case ...
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### How can I use a magnet to lift a paperclip?

This question has been asked already, but no satisfying answer came up. All the answers seem to push the problem further, but do not explain clearly what is going on. I will reformulate it for a ...
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### Why do we obtain classical physics by taking the limit of Planck's constant to zero?

Why if we specifically set Planck's constant equal to zero (the limit of it) do we sometimes get classical physics? I mean, what does it mean physically to set the constant equal to zero? Or to say it ...
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### Relativistic time dilation on Mars compared to Earth?

What is the time dilation in Mars, compared to earth? Can we accurately calculate it? What information is needed to do these calculations?
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### How to add Langevin terms to the semiclassical Bose-Hubbard model?

I would like to add Langevin terms to the Hamilton equations of motion of the semiclassical Bose-Hubbard model. Here's what I have: I start with the standard example of Brownian motion, a particle ...
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### What determines the Bloch wavepacket length scale?

We know in the semiclassical Boltzmann theory, there are several length scales: the lattice constant $a$, the Bloch wavepacket spread $\xi$, other length scales such as the mean free path $l$, the ...
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### Planck's constant and phase space in quantum mechanics

During my undergrad physics classes, I've come across several seemingly related phenomena dealing with $h$ and phase space in quantum mechanics. Let $T_x$ be a translation operator by $x$ in ...
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### Probability conservation in WKB tunneling

Suppose we have quantum mechanical plane waves of energy $E$ incident upon a one-dimensional potential barrier $V(x)$ with sloping sides. One can compare the WKB solutions in the three relevant ...
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### What exactly is closed orbit theory and what assumptions go into it?

I am just beginning a research project on the study of closed orbits, specifically as related to hydrogen, and I wanted a little bit more information on what exactly makes something a "closed orbit". ...
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### Classical spin viewed as $SU(2)$

In which sense is the configuration variable of a classical spin $SU(2)$? I can view a classical spin as a unit vector in $\mathbb{S}^2$ (2-dim. sphere), but it seems it is really given by a matrix $U$...
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### WKB boundary conditions [duplicate]

Technically, this is a math problem but I think it is better here than in the math stacks. Consider the differential equation $$y'' = (x^4 - E)y$$ The boundary ...
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### What is a 'turning point' in WKB and why does it fail at that point?

What is meant by a classical turning point in quantum mechanics and why does the WKB approximation fail at that point?
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### bohr-sommerfeld quantiztion condition from semiclasical WKB

in WKB the quantization conditions are $$\oint _{C} p.dq =2\pi n \hbar \tag{1}$$ and the wave function is $$\Psi(x)= exp \left( \frac{iS[y(x)]}{\hbar} \right), \tag{2}$$ but what boundary ...