All Questions
Tagged with hamiltonian energy
141
questions
8
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4
answers
1k
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Examples of systems with infinite dimensional Hilbert space, whose energy is bounded from above
We often encounter (and love to!) deal with systems whose energy is bounded from below, for good reasons like stability, etc. But what about systems whose energy is bounded from above? In finite ...
- 785
0
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0
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38
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Mean energy measurement in an arbitrary quantum state
I've gone through many papers looking for a way to measure a mean energy in an arbitrary state $\langle \psi | H | \psi \rangle$. I am interested in a theoretical protocol or an exemplary experimental ...
- 1
0
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0
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29
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Fourier transform of spinless $t$-$V$ model for $t=0$
I am trying to compute the Fourier transform of the 2D $t$-$V$ model for the case $t=0$.
\begin{equation}
\hat H = -t \displaystyle \sum_{\langle i,j\rangle} ( \hat c_i^{\dagger} \hat c_j + \hat c_j^{...
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4
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4
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How can the Klein-Gordon equation have negative-energy solution if its Hamiltonian is positive-definite?
In a lesson about the introduction of classical field theory it was mentioned the Klein-Gordon equation
$$(\Box + m^2) \phi(x) = 0. \tag{1}$$
But before we got this equation, we studied the ...
- 111
1
vote
2
answers
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Complex potential in quantum mechanics
I'm reading Quantum Mechanics by Griffiths. In the solution to one of the problems in this book they claimed that if the time-independent wavefunction $\psi$ solves $-\frac{\hbar}{2m}\frac{\partial^2\...
- 353
0
votes
2
answers
135
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Proof/Explanation for why the Hamiltonian operator's eigenvalues are the permitted energy values? [closed]
I'm looking for a proof as to why the Hamiltonian operator's eigenvalues in quantum mechanics are the permitted energies of a quantum particle. I am looking for an intuitive explanation as well as a ...
- 799
1
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2
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Why is there an energy difference of $\hbar$ between spin up and spin down?
In Griffith's Introduction to Quantum Mechanics he describes the operators related to spin-$1/2$ particles in chapter 4. One of those operators is
$$
\hat{S}_z=\frac{\hbar}{2}\hat{\sigma}=\frac{\hbar}{...
- 55
4
votes
8
answers
497
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For a classical scalar field, how can a mode have different energies if the energy is the mode's frequency of oscillation in time?
For a classical real scalar field $\phi(\vec{x},t)$ of the type:
$$\frac{\partial^2\phi}{\partial t^2}-\nabla^2\phi+m^2\phi=0$$
The modes $\phi(\vec{p},t)$ can be obtained by:
$$\phi(\vec{x},t)=\int \...
- 454
8
votes
1
answer
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If the Lagrangian depends explicitly on time then the Hamiltonian is not conserved?
Why is the Hamiltonian not conserved when the Lagrangian has an explicit time dependence? What I mean is that it is very obvious to argue that if the Lagrangian has no an explicit time dependence $L=L(...
- 227
1
vote
4
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613
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Hamiltonian Operator
I've learned that the Hamiltonian Operator corresponds to the total energy of the system when applied to a general wave function. After applying and obtaining the measurement (energy), the wave ...
user381511
0
votes
0
answers
48
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Hamiltonian being Total Energy [duplicate]
From what I’ve studied till now, Hamiltonian was initially introduced as some quantity that is usually conserved in a system and it can be total energy and it can’t either. If it is not fixed if it is ...
1
vote
0
answers
45
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Why energy eigenstates are extrema of the energy functional? [duplicate]
We have the energy functional of a system:
$$E[\psi] = \frac{\langle \psi | \hat{H} | \psi \rangle}{\langle \psi | \psi \rangle}$$
and over numerous textbooks it is said that the eigenstates of the ...
2
votes
2
answers
161
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Calculating the energy using path integrals vs hamiltonian
I'm reading A. Zee's "Quantum Field Theory in a Nutshell" section I.4 in which he used path integrals to calculate the energy of a real scalar field and 2 sources depending only on the ...
- 1,324
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0
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Energy Operator, Hamiltonian, Energy Eigenvalues [duplicate]
Can we use the energy operator $i\hbar\frac{\partial}{\partial t}$ instead of the Hamiltonian to obtain the energy eigenvalues?
1
vote
1
answer
52
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Hamiltonian energy $E=H = -\frac{\partial S}{\partial t}$ [closed]
In most of the cases, the Hamiltonian is equal to the total mechanical energy, which is usually conserved. They are equal and conserved when the potential energy is not dependent on velocity and there ...
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