All Questions
Tagged with hamiltonian quantum-mechanics
1,075
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Hamiltonian of a system? [closed]
I have a three level lambda system with two ground states $\lvert1\rangle$ and $\lvert3\rangle$ and an excited state $\lvert2\rangle$, interacting with a classical field and the SPP mode of the ...
- 11
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1
answer
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Relationship between unitaries generated by a Hamiltonian and its negative sign
Consider two unitary operations $U_1$ and $U_2$ defined by:
$\partial_t U_1 = -iH_1U_1$ and $\partial_t U_2 = iH_1U_2$
Here, $U_1$ is generated by $H_1$ and $U_2$ is generated by $-H_1$, with the ...
- 83
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How to get a lower bound of the ground state energy?
The variational principle gives an upper bound of the ground state energy. Thus it is quite easy to get an upper bound for the ground state energy. Every variational wave function will provide one.
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- 1,957
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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
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In degenerate perturbation theory why can we assume that matrix elements above and below the degenerate subspace disappear?
The picture shows some original Hamiltonian H which has some degeneracies. Suppose I have some perturbation V to the system and I want to find the new energies and eigenstates of the system. Then from ...
- 103
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Solving for unitary operation using perturbation theory
Let the time-dependent Hamiltonian be
\begin{equation}
H(t) = H_0(t) + \lambda H_1(t),
\end{equation} where $\lambda$ is a small parameter. In the interaction picture (i.e. rotating frame w.r.t ...
- 93
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Are "good" states in perturbation theory eigenstates of both the unperturbed and perturbed Hamiltonian?
In my quantum course, my professor asked us the true/false question:
"Are 'good' states in degenerate perturbation theory eigenstates of the perturbed Hamiltonian, $H_0 + H'$?"
I was ...
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What are the similarities and differences between the Magnus expansion and the Schrieffer-Wolff transformation?
The Magnus expansion and the Schrieffer-Wolff transformation are both methods used to get certain effective Hamiltonians. I know that at a basic level, the Schrieffer-Wolff transformation eliminates ...
- 19
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2
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Energy and momentum operators using Hamilton's equations
The energy operator is:
$${\displaystyle {\hat {E}}=i\hbar {\frac {\partial }{\partial t}}}\tag1$$
and the momentum operator is
$${\displaystyle {\hat {p}}=-i\hbar {\frac {\partial }{\partial x}}}.\...
- 443
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Eigenstates of the Laplacian and boundary conditions
Consider the following setting. I have a box $\Omega = [0,L]^{d} \subset \mathbb{R}^{d}$, for some $L> 0$. In physics, this is usually the case in statistical mechanics or some problems in quantum ...
- 1,131
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Are $\mathcal{PT}$-symmetric Hamiltonians dual to Hermitian Hamiltonians?
I was reading this review paper by Bender, in particular section VI where they show that, despite $\mathcal{PT}$-symmetric Hamiltonians not being hermitian, they can have a real spectra. They go on ...
- 1,544
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Existence of eigenstates in the context of continuous energies in the Lippmann-Schwinger equation
In the book QFT by Schwartz, in section 4.1 "Lippmann-Schwinger equation", he says that:
If we write Hamiltonian as $H=H_0+V$ and the energies are continuous, and we have eigenstate of $H_0$...
- 57
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How do I formulate a quantum version of Hamiltonian flow/symplectomorphisms in phase space to have a "geometric", quantum version of Noether's theorem
I'm currently exploring how Noether's theorem is formulated in the Hamiltonian formalism. I've found that canonical transformations which conserve volumes in phase space, these isometric deformations ...
- 111
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Why is the time derivative of the wavefunction proportional to a linear operator on it? [closed]
I am currently trying to self-study quantum mechanics. From what I have read, it is said that knowing the wave function at some instant determines its behavior at all feature instants, I came across ...
- 23
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How Can I find Free Hamiltonian for this Problem?
I have got an Open Quantum System in which two two level atoms (two identical qubits) interact separately with two independent environments in the presence of the ...
