Questions tagged [hamiltonian]
The central term in the hamiltonian formalism. Can be interpreted as an energy input, or "true" energy.
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Property of the Hamiltonian's discrete spectrum
I have found a statement online saying that there must be an eigenvalue of the Hamiltonian inside the range $(E-\Delta H,E+\Delta H)$. Where the mean value and variance are defined for a random (...
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Schrodinger equation with $\hbar =1$
The Schrodinger equation is given by:
$$i \hbar \frac{d}{dt}|\psi(t)\rangle = H(t)|\psi(t)\rangle.$$
Sometimes, physicists set $\hbar=1$. I suppose that they achieve this by changing the scaling and ...
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If $H$ anniliates a state, must $Q$ and $Q^\dagger$ also annihilate the state?
Suppose we have a a Hamiltonian, $H$. And suppose also we have some operator $Q$ such that $\{Q, Q^{\dagger}\} = H$, and $Q^2 = 0$.
If we find a state $|\psi \rangle$ such that $Q|\psi \rangle = Q^{\...
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Is it possible to formulate classical Hamiltonian mechanics without reference to a Lagrangian? [duplicate]
The typical way to arrive at Hamiltonian mechanics is through Lagrangian mechanics, defining canonical momentum and the hamiltonian itself in reference to the Lagrangian and its derivatives, but I'm ...
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Why are these unbounded operators (essentially) self-adjoint?
Can anyone provide exact mathematical reasoning as to why the following fundamental unbounded symmetric operators are essentially self-adjoint? I.e. on, their natural domains, they admit a unique ...
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Defining the Problem Hamiltonian for Quantum Annealing in Solving the Shortest Path Problem [closed]
I’m currently studying quantum annealing and its application to solving the shortest path problem. However, I’m facing challenges in defining the problem Hamiltonian, whose ground state should encode ...
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Why does the Dyson series have a 1/n! factor?
This is the explanation from Wikipedia:
Is there a more rigorous proof or explanation of how reducing the integration region to these sub-regions introduces a $\frac{1}{n!}$ factor? I am confused ...
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The time-derivative of the Hamiltonian for a 1D harmonic potential [closed]
I do not understand how to take the time derivative of the following Hamiltonian $\hat{H}(t) = \frac{\hat{p}^2}{2m} + \frac{1}{2}m\omega^2(\hat{x}-a(t))^2$, where $a(t) = v_0t$. For instance how does ...
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Possible inconsistencies of the Hamiltonian in the two-body problem
When we solve the single coordinate Schrödinger equation,
\begin{equation}
i \hbar \partial_t \psi = - \frac{\hbar^2}{2 \ m} \ \nabla^2 \psi \ + \ V(x) \ \psi, \tag{1}
\end{equation}
we imply the ...
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Is there a name for a Heisenberg-like model, but instead of the ZZ operator, we have one that favor only spin-up-spin-up configurations?
I understand that the Quantum Heisenberg XXZ model in 1D has the form:
$$\hat H = \frac{1}{2} \sum_{j=1}^{N} (J_x \sigma_j^x \sigma_{j+1}^x + J_y \sigma_j^y \sigma_{j+1}^y + J_z \sigma_j^z \sigma_{j+1}...
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Identifying avoided crossings
Consider the following spectrum
This spectrum represents the evolution of the energy levels of a certain molecule in its ro-vibrational ground state as a function of the magnetic field.
Such graphs ...
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How can the Klein-Gordon equation have negative-energy solution if its Hamiltonian is positive-definite?
In a lesson about the introduction of classical field theory it was mentioned the Klein-Gordon equation
$$(\Box + m^2) \phi(x) = 0. \tag{1}$$
But before we got this equation, we studied the ...
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Does the Hamiltonian for a quantized EM field neglect non-radiate field?
Suppose positive and negative charges are separated into different objects by friction in some inertial lab frame. Those objects are then moved to opposite directions along the $x$ axis, with an ...
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How the supercharge operators act on superfields in quantum mechanics, and the adjoints of supercharges?
I'm watching this lecture on introductory Supersymmetry (Clay Cordova, 2019 TASI lecture 2 on Supersymmetry). My question relates to the first 20minutes or so. The lecturer is introducing Superfields ...
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Classical mechanics: Hamiltonian perturbation theory. What if the perturbing parameter is < 0?
In Hamiltonian Perturbation theory, we have a Hamiltonian of the form $$H(q,p) = H_0(q,p) + \lambda H_1(q,p).$$
One proceeds by expanding the equations of motion in powers of $\lambda$, assuming $\...
