Linked Questions
16 questions linked to/from Example where Hamiltonian $H \neq T+V=E$, but $E=T+V$ is conserved
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Energy conservation Hamiltonian dependency [duplicate]
Suppose the a system has a Hamiltonian $H = H(q,p)$, and suppose $H$ does not depend explicitly on time. If $H\neq E$ the total energy of the system, does this necessarily say that $E$ is not ...
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When is the Hamiltonian of a system not equal to its total energy?
I thought the Hamiltonian was always equal to the total energy of a system but have read that this isn't always true. Is there an example of this and does the Hamiltonian have a physical ...
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Bead on a rotating hoop: Hamiltonian is conserved, but is not the total mechanical energy
Consider a bead (mass $m$) on a frictionless hoop (radius $R$) in the presence of gravity. The hoop is spun around an axis parallel to the gravitational acceleration at constant angular speed ($\omega$...
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Why is the Hamiltonian zero in relativity?
I'm trying to understand something with the lagrangian and the hamiltonian formalisms in relativity theory, and why the following result cannot be the same in classical (non-relativistic) mechanics. ...
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What is a gauge theory?
Please note that I just read about 20 forum discussions, none of which answered my question. This question is related to my earlier question Is spacetime symmetry a gauge symmetry?.
I am looking for ...
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Is it obvious that the Hamiltonian observable in Quantum Mechanics should also be the Energy observable?
In Quantum Mechanics, the Hamiltonian observable is defined as the generator of time translations. It's easy to show that if we take this to be the definition of the Hamiltonian, then it is of the ...
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Can you find a physical system with $T=-V$?
Can you find a physical system with $T=-V$, with $T$ the kinetic energy
and $V$ the potential energy, i.e., $H=0$ for the system? (Not for a point of time but for the whole time.)
What about $L=\...
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Why is the Hamiltonian of a photon = 0?
I'm studying the motion of light near Schwarzschild black holes, and I was wondering why the Hamiltonian of the Schwarzschild metric $$H = - \left( 1-\frac{2M}{r} \right)^{-1} \frac{p_{t}^2}{2}+\left(...
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Is the Wheeler deWitt equation consistent with the holographic principle?
In this paper by Sean Carroll (What if Time Really Exists), there's a section "Lessons from Duality" where he says that the holographic principle (and in particular, that a lower dimensional non-...
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What is energy in quantum mechanics?
Is it wrong to say energy is the expectation value of Hamiltonian?
Or should I say energy is the eigenvalue of Hamiltonian?
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Is $H = T + U$ for a pendulum on a circle movement?
I have this problem:
Obtain Hamilton's equations of motion for a plane pendulum of length $l$ with mass point $m$ whose radius of suspension rotates uniformally on the circumference of a vertical ...
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Canonical momentum not observable vs energy is observable
I have seen explanations that canonical momentum for charged particles $p = mv + qA/c$ is not a measurable quantity/observable because it is not gauge invariant. However, there are many quantities ...
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Is expectation value of the Hamiltonian always the energy? [duplicate]
There are time dependent & space dependent systems (magnetic fields) and time independent (particle in a box or harmonic oscillator). In the latter the expectation value is the 'average' energy ...
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Imaginary part of complex non-Hermitian Hamiltonians
I have just started studying the $PT$-symmetric and non-hermitian hamiltonians.
But I am not able to interpret the imaginary part of the hamiltonian. If Hamiltonian is basically the total energy of ...
user274797
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The problem of time in classical general relativity
It is well known that the Hamiltonian of General Relativity is a linear combination of constraints. This poses a challenge in quantum gravity. If a state $\psi$ solves the constraints ($\hat C_\alpha \...
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