All Questions
Tagged with hamiltonian linear-algebra
34
questions
1
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1
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131
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Understanding equation for eigenvalues of a Hamiltonian
I'm reading the paper Hamiltonian Truncation Study of Supersymmetric
Quantum Mechanics. I'm not understanding a claim they make about the eigenvalues of a certain Hamiltonian. In particular, how eqn 3....
- 213
1
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0
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63
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Identifying avoided crossings
Consider the following spectrum
This spectrum represents the evolution of the energy levels of a certain molecule in its ro-vibrational ground state as a function of the magnetic field.
Such graphs ...
- 197
2
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1
answer
95
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Is the Hamiltonian for the transverse field Ising model Hermitian?
I'm watching these lectures in Condensed Matter Physics. At Lec. 13, the lecturer introduces the transverse field Ising model with the Hamiltonian
$$H = - J \sum_i \sigma_i^x \sigma_{i+1}^x - h \sum_i ...
- 22.1k
0
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1
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88
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Implementation of Hamiltonian coupling to a bath
I want to study a system coupled to a bath, however I do not fully understand how to implement/think of the Hamiltonian. For simplicity say the bath is given by a spin chain (PBC), e.g. Ising-like
$$...
- 13
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2
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169
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Relation between eigenvalue equation for an operator and for its square
Consider a time indipendent Schrodinger problem:
$$\hat{H}\psi_E(p) = E \psi_E(p)$$
with suitable boundary conditions.
We know that $\psi_E$ are the eigenfunctions of $\hat{H}$.
If we now consider the ...
- 1,611
1
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1
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115
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Why $\sum_n|E_n \rangle \operatorname{exp}(-\beta\mathcal{H})\langle E_n| = \operatorname{exp}(-\beta \mathcal{H})$? (Quantum statistics)
I am reading James P. Sethna, Statistical Mechanics : Entropy, Order Parameters, and Complexity, p.137 and stuck at some equality. I think that this question is like homework-question ( In fact this ...
- 323
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0
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52
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Perturbation theory: Why is the inner product expressed as $\langle\psi_m^0|H'|\psi_n^0\rangle=-2V_0(-1)^{\frac{m+1}{2}}$? [closed]
Introducing a perturbation to an unperturbed state, say $\psi_n^0$, with eigenenergy $E_n^0$ yields the first degenerate state as:
$$\psi_n^1=\sum_{m\neq n}\frac{\langle\psi_m^0|H'|\psi_n^0\rangle}{(...
- 461
1
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1
answer
53
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Huckel model of periodic systems
I have a polymer that is approximated by linear chain model. I need to solve the eigenvalue problem with such infinite dimensional hamiltonian matrix and ansatz $c_n = Asin(kna)$, where $k=\dfrac{2\pi}...
- 15
-1
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1
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207
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Hamiltonian as a matrix and its elements [closed]
Let us consider an electron in an infinitely deep one-dimensional potential well of thickness L with zero potential energy at the bottom of the well. The normalised eigenfunction solutions to this can ...
- 131
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2
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180
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How do I diagonalize this Hamiltonian? [closed]
I have a Hamiltonian
$$H = \frac{p^2}{2}+\frac{\omega^2 q^2}{2}+\frac{\gamma}{2}(qp + pq)$$
which I have to diagonalize, i.e., find $a$ and $a^\dagger$ as linear combinations of cannonical $p$ and $q$ ...
- 904
4
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3
answers
793
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Diagonalising the Hamilton operator, why does this magic work?
Let the Hamilton operator $H= \omega_1 a_1^\dagger a_1 + \omega_2 a_2^\dagger a_2 + \frac{J}{2} (a_1^\dagger a_2 + a_1 a_2^\dagger)$ be given, of course $a_j$ and $a_j^\dagger$ are the creation and ...
- 870
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1
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137
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How to solve for the scattering solution of following Schrodinger equation?
Suppose you have non-relativistic fermions scattering off a delta function potential.
It is an easy job to solve $H=-\partial_x^2+\epsilon \delta(x)$ by starting with an eigenfunction of the form $\...
- 243
9
votes
1
answer
562
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Are the instantaneous eigenstates of a time-dependent hamiltonian continuous?
I am trying to understand the adiabatic theorem. I can follow the proofs that are given in Wikipedia (https://en.wikipedia.org/wiki/Adiabatic_theorem) but there seems to be a hidden assumption.
For a ...
- 352
3
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0
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178
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Eigenkets of a two-state hamiltonian
I have a question related to this other question: Eigenenergies and eigenkets given the Hamiltonian. In it, OP is given the following hamiltonian:
$$
H=a(|1\rangle \langle1|-|2\rangle\langle2|+|1\...
- 43
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2
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268
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Why are Eigenvectors of a 1D quantum ising hamiltonian real
I was modelling the 1D transverse quantum Ising model and made a Kronecker product loop to find the Hamiltonian of the system, for a given magnetic field configuration. Now, my question is that when I ...
