Tagged Questions

The central term in the hamiltonian formalism. Can be interpreted as an energy input, or "true" energy.

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What is the meaning of commuting Hamiltonians?

I have two quantum mechanical Hamiltonians such that $$[\hat{H}_1,\hat{H}_2] = 0,$$ where $\hat{H}_1$ and $\hat{H}_2$ act on the same set of states. What is there to ...
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Hamiltonian matrix off diagonal elements?

I'm trying to understand how Hamiltonian matrices are built for optical applications. In the excerpts below, from the book "Optically polarized atoms: understanding light-atom interaction", what I don'...
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Conjugate Transpose of Hamiltonian Matrix

I read some notes saying, $$i\hbar \frac{dC_{i}(t)}{dt} = \sum_{j}^{} H_{ij}(t)C_{j}(t)\tag{1}$$ where $C_{i}(t) = \langle i|\psi(t)\rangle$ and $H_{ij}$ is hamiltonian matrix. However, what is ...
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Quantum Mechanics: Relate solutions for two dual hamiltonians?

Consider a Hamiltonian in quantum mechanics: $$H_x=-\frac{d^2}{dx^2}+V(x,c)$$ where $x\in\mathbb{R}$ and the potential $V(x,c)$ depends on position $x$ and a continuous parameter $c$. Furthermore, ...
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How would Hamiltonian for several fermions with spin look?

All discussions of Pauli exclusion principle I read usually talked about antisymmetric wavefunctions, from which the princinple appears. But I would like to see a Hamiltonian for multiple fermions, ...
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How to get Hamiltonian of QED from lagrangian?

I have the QED lagrangian: $$L = \bar {\Psi}(i \gamma^{\mu }\partial_{\mu} + q\gamma^{\mu}A_{\mu} - m)\Psi + \frac{1}{16 \pi}F_{\alpha \beta}F^{\alpha \beta} .$$ I tried to get hamiltonian by ...
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When Hamiltonian and the total energy are the same

In which condition, the Hamiltonian is the same as the total energy of the system, or say $H=T+V$?
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Temperature in the Hamiltonian limit

There is a well known connection between statistical mechanics in D spatial dimensions and quantum field theory in D-1 spatial dimensions. Changing the temperature in statistical mechanics corresponds ...
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Using Dyson formula in Schrodinger picture

From Time-ordering and Dyson series and what I learnt, Dyson formula is used in the situation of interaction picture: $$i\frac{dU_I}{dt} = H_{I}(t)U_I$$ where $H_I(t)$ is interaction Hamiltonian ...
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Is there any Hamiltonian that contains time derivative? [duplicate]

Quantum mechanics is governed by Schrodinger's equation: $$\hat{H}\psi=i\hbar\partial_t \psi$$ It seems that Hamiltonian acts on wave functions like a time derivative. Just out of curiosity, is ...
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How to include Berry connection in Hamiltonian?

When we calculate Berry connection, $A(R)=i<\psi(x,y)|\frac{d}{dR}|\psi(x,y)>\hat{R}$ corresponding to the Berry phase of any system, the gauge potential is related to the $R$ of the parameter ...
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Quantum mechanics with non-cartesian coordinates

Let say we have the classical hamiltonian of a harmonic oscillator: $$H=\frac{p_x^2+p_y^2+p_z^2}{2m}+\frac{k_1x^2+k_2y^2+k_3z^2}{2}$$ and we want to find the hamiltonian operator in quantum mechanics, ...
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Feynman's $i \epsilon$ prescription in loop expansion

I have some questions about the $i\epsilon$ factor in Feynman diagrams. First, what is the physical meaning of $i\epsilon$ in loop amplitudes. Second, how does it ensures unitarity? And third, Dyson ...
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Eigenenergies and eigenkets given the Hamiltonian

For a two level system the Hamiltonian is: $$H=a(|1\rangle \langle1|-|2\rangle\langle2|+|1\rangle\langle2|+|2\rangle\langle1|)$$ where $a$ is a number with the dimension of an energy. I need to ...
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Alkali atom in oscilating electromagnetic field

I am trying to calculate atom - light (EM field) interaction Hamiltonian, and the results I get seem to me rather unphysical - I get some nonzero matrix elements which should not be there. Please, can ...
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It seems to me that superpotentials can be defined in a theory with or without supersymmetry. Is this true?

I recently read "An Introduction to Supersymmetry in Quantum Mechanical Systems" by T. Wellman (amongst other sources) in an effort to find out what a superpotential actually is and how it relates to ...
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Is there a valid Lagrangian formulation for all classical systems?

Can one use the Lagrangian formalism for all classical systems, i.e. systems with a set of trajectories $\vec{x}_i(t)$ describing paths? On the wikipedia page of Lagrangian mechanics, there is an ...
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How to write the Fröhlich Hamiltonian in one dimension?

I am currently working on a (functional) analysis problem refining Pekar's Ansatz (or adiabatic approximation, as it is called in his beautiful 1961 manuscript "Research in Electron Theory of Crystals"...
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How I can prove the Commutation between hamiltonian and Runge-Lenz vector? [closed]

I am a undergraduate student in physics. I found this page that shows a way to prove the commutator between Runge-Lenz vector and Hamiltonian .$\left [\hat{A}_{i},\hat{H}\right]=0$ I believe he did a ...
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