# Tagged Questions

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### What's the value of the coupling constant in interacting field theories?

Consider this Lagrangian : $L = \frac{1}{2}(\partial_\mu \Phi)^2 - \frac{M^2}{2}\Phi^2 +\frac{1}{2}(\partial_\mu \phi)^2 -\frac{m^2}{2} \phi^2 -\mu\Phi\phi^2$ Its interaction term is given by : ...
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### Difference between Hamiltonian in classical Mechanics and in quantum Mechanics

I have a question about difference between Hamiltonian function (the description of system in classical physics) and the Hamiltonian operator (quantum mechanics). I think that there two different ...
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### Examples of Weyl transforms of nontrivial operators

I've been able to find examples of Weyl transforms of operators like $\hat{x}$,$\hat{p}$, and $\hat{1}$, but not anything more complicated. Are there derivations of the Weyl transforms of more ...
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### Schroedinger equation. Why Potential energy instead of Force?

What is the reason Schroedinger equation is quoted in terms of potential energy instead of force?
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### Degenerate perturbation theory applied to topological degeneracy?

Consider a quantum system described by a gapped Hamiltonian $H_0$ with degenerate ground states (GS), adding a perturbation term $V$ to $H_0$, then the low-energy physics can be described by an ...
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### Why don't we use Hamilton-Jacobi method in QM?

In classical mechanics, we usually try to find a set of coordinates by Hamilton-Jacobi method to transform the Hamiltonian to zero such that the coordinates are conservations. However, we never try ...
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### Gauge Invariance of the Hamiltonian of the electromagnetic field

The Hamiltonian for an electron of mass $m$ and charge $e$ in an exterior electromagnetic field is $$H=\frac{1}{2m}(p-(e/c)A)^2+e\varphi.$$ The corresponding (via canonical quantization) quantum ...
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### Do we have a fundamental Hamiltonian for the system of H$_2$O molecules?

From the quantum mechanics(QM) viewpoint, does there exist a Hamiltonian $H$ for the system of H$_2$O molecules? Assume that the number of H$_2$O molecules is fixed. Imagine that by calculating the ...
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### Why not formulate Quantum Mechanics using Lagrangians? [duplicate]

As the title implies, why is it that the most common formalisms we use in quantum mechanics prefer to describe systems in the terms of a Hamiltionian instead of a Lagrangian? Is there some ...
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### Why are we living in the $q$ part of the phase space?

In Hamilton mechanics and quantum mechanics, $p$ and $q$ are almost symmetric. But in the real world, the $p$ space isn't as intuitive as the $q$ space. For example, We can uniquely identify a person ...
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### Constructing a Hamiltonian (as a polynomial of $q_i$ and $p_i$) from its spectrum

For a countable sequence of positive numbers $S=\{\lambda_i\}_{i\in N}$ is there a construction producing a Hamiltonian with spectrum $S$ (or at least having the same eigenvalues for $i\leq s$ for ...
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### Conjugate Variables and Fourier Transforms in Classical Physics

Let q be a generalized coordinate with a conjugate momentum p and a potential resulting in a periodic motion of q. What is the meaning of the Fourier transform of q(t) over its period? Can this be ...
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### Degeneracy and the Hamiltonian

How many linearly independent eigenfunctions can be associated with one degenerate eigenvalue of the Hamiltonian operator? (Is there a limit since it contains a 2nd order differential operator?) ...
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### Connections of iterative solvers for large systems of equation in Physics?

I am trying to find the domains in physics where solving large systems of equations is computationally expensive. The sparse systems are of my particular interest, where the input matrix A is in GBs ...
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### Energy operator

Does the Hamiltonian always translate to the energy of a system? What about in QM? So by the Schrodinger equation, is it true then that $i\hbar{\partial\over\partial t}|\psi\rangle=H|\psi\rangle$ ...
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### Sudden change in the Hamiltonian

Could someone explain what this sentence mean? "If the Hamiltonian changes suddenly by a finite amount, the wavefunction must change continuously in order that the time-dependent Schrodinger equation ...
Is there any significance to: $\langle[H,\hat{O}]\rangle =0$ (which can easily be shown) where $H$ is the Hamiltonian, $\hat{O}$ is an arbitrary operator? Thanks.
### interpretation of $\{H,L^2\}$
In Hamiltonian mechanics, we show $\{H,L_z\}=0$, which can be interpreted as the conservation of angular momentum around $Oz$. Following the same idea, how can we interprete $\{H,L^2\}$? Is the ...