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3 days ago · An example of an eigenvalue equation where the transformation is represented in terms of a differential operator is the time-independent Schrödinger equation in quantum mechanics: H ψ E = E ψ E {\displaystyle H\psi _{E}=E\psi _{E}\,}
3 days ago · Although has the dimension of time, it is different from the time parameter t that enters the Schrödinger equation. This τ B {\displaystyle \tau _{B}} can be interpreted as time for which the expectation value of the observable, B ^ , {\displaystyle \langle {\hat {B}}\rangle ,} changes by an amount equal to one standard deviation ...
2 days ago · In the Schrödinger equation for this system of one negative and one positive particle, the atomic orbitals are the eigenstates of the Hamiltonian operator for the energy. They can be obtained analytically, meaning that the resulting orbitals are products of a polynomial series, and exponential and trigonometric functions .
3 days ago · Quantum mechanics, science dealing with the behavior of matter and light on the atomic and subatomic scale. It attempts to describe and account for the properties of molecules and atoms and their constituents—electrons, protons, neutrons, and other more esoteric particles such as quarks and gluons.
2 days ago · The nonlinear Schrödinger equation (NLSE) is a fundamental model in physics relevant to fields such as nonlinear optics, Bose–Einstein condensates, and fiber optics. This study explores the fascinating realm of optical solitons, bifurcation analysis, and chaotic behaviors that result from the NLSE with cubic-quintic-septic-nonic nonlinearity of self-phase modulation. First, we transform the ...
4 days ago · The term “gravitational atom” is not a stretch. The cloud’s evolution is described by the Schrödinger equation and the energy levels are hydrogen-like in the nonrelativistic limit. Fully grasping the impact of gravitational atoms on binary evolution is an intricate problem even in the simplest possible scenario.
3 days ago · We study the propagation properties of abstract linear Schrödinger equations of the form i∂tψ = H0ψ + V(t)ψ, where H0 is a self-adjoint operator and V(t) a time-dependent potential.
