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Results tagged with quantum-mechanics
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user 212731
Quantum mechanics describes the microscopic properties of nature in a regime where classical mechanics no longer applies. It explains phenomena such as the wave-particle duality, quantization of energy, and the uncertainty principle and is generally used in single-body systems. Use the quantum-field-theory tag for the theory of many-body quantum-mechanical systems.
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How does the measure of purity of a mixed state evolve with time in quantum mechanics?
We know that the Tr() is invariant with respect to unitary transformation. So does the density matrix $\rho(t)$ does not evolve with time?
$\begin{align} \ \rho(t) =&|\psi(t)\rangle \langle \psi(t) …
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What are the ways to carry out time propagation numerically?
There are many ways to solve the time-dependent Schrodinger equation (TDSE) and find the wavefunction $|\Psi(t)\rangle$ for a given Hamiltonian. For example, consider a tight binding type Hamiltonian: …
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What is line broadening phenomenon in quantum many body physics?
I have been reading Anderson's paper, "Absence of diffusion in a certain Random Lattice" and found the concept of inhomogeneous broadening. I couldn't really find a satisfactory explanation with a val …
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Iterative block diagonalisation in degenerate perturbation theory
How is iterative block diagonalisation carried out in the matrix form of degenerate perturbation theory to lift degeneracy present in the zeroth-order or unperturbed Hamiltonian ($H_{0}$)? In general …
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Tracing $\rho (t)$ with respect to the Bath when system and bath are coupled in an open quan...
Consider a system S that is coupled to a bath B. Let {$|s_i\rangle 's$} and {$|b_j\rangle 's$} be the eigen states of the system and bath hamiltonians respectively (i.e)
\begin{align}
\hat{H}_{S}|s_i …
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Does the phase of an electronic ground state wavefunction matter in a numerical calculation?
Does the phase of wavefunction matter in a numerical calculation?
Recently, I was trying to solve a simple model system using numerical grid-based methods and saw that the phase of the ground state wa …
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Importance of analytic solutions to Hamiltonians
Why is it important to attempt to find an analytic solution for any theoretical model? It usually happens that many of the hamiltonians written to model the system may not usually have exact solutions …
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Diagonalization of a matrix with operators as elements
How to diagonalize a hamiltonian matrix that has differential operators as elements? My matrix looks something like:
\begin{bmatrix}
A \frac{d^{2}}{{d\theta}^{2}}+ B_{1} & a\cos{(b\theta +c)}\\
a\cos …
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Resource recommendation for time-dependent DMRG
I am looking for any references (journal article/ review /tutorial) to understand the TEBD (Time-evolution by block decimation) algorithm and code it up for a simple 1D model system. Broadly, I am in …
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Why can $|\Psi (t=0)\rangle $ be written as a coherent superposition of some eigenkets?
Why can $|\Psi (t=0)\rangle $ be written as a coherent superposition of some eigenkets?
One of the approaches to solve time dependent Schrodinger equation $i\hbar \frac{\partial |\Psi(t)\rangle}{\par …
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Quantum mechanics Dirac delta representation with integral
You can just rewrite the integral first(make substitutions $x = -x$, $\frac{p}{\hbar}=k$), say $$I=\int_{-\infty}^{\infty}dx \ e^{-i k.x} e^{-ax^2}$$
Now, this is a like a Fourier transform of a Gauss …
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Generalised basis independent relationship between Von Neumann Entropy and Purity of a quant... [duplicate]
I have been trying to find a generalized relationship between Von Neumann Entropy and Purity of a quantum state? In this post there is a discussion of a specific case for a qubit and a more general ca …
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Hamiltonian Operator
The process of measurement, leads to a collapse of the wave function to one of the eigenstates with a certain probability. The eigen basis which gives this probability distribution is definitely relat …
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How do we derive the minimal coupling Hamiltonian?
Is there a way to rigorously derive the minimal coupling hamiltonian for a system interacting with electromagnetic radiation. How de we arrive at the expression:
$$\hat{H} = \frac{1}{2m}(p-\frac{q}{c} …
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