Hydrogen atom in phase space: the Wigner representation
... for the 1s state of the hydrogen atom. In the literature one can find only a limited number of papers devoted to this subject that are based on approximate methods [5, 6], and the only other published result has generated controversies [7]. In a different context, the hydrogen atom has been investig ...
... for the 1s state of the hydrogen atom. In the literature one can find only a limited number of papers devoted to this subject that are based on approximate methods [5, 6], and the only other published result has generated controversies [7]. In a different context, the hydrogen atom has been investig ...
On the conundrum of deriving exact solutions from approximate
... these variables, the same is true for the cumulants in Eq. (37) and, consequently, only the terms with ‘ = 1, 2 contribute to this expansion. Evaluating the expansion coefficients explicitly, one finds that they are identical to those of the second-order time-local master equation (15). The equivalence ...
... these variables, the same is true for the cumulants in Eq. (37) and, consequently, only the terms with ‘ = 1, 2 contribute to this expansion. Evaluating the expansion coefficients explicitly, one finds that they are identical to those of the second-order time-local master equation (15). The equivalence ...
R-107_WangCY.pdf
... GREEN’S FUNCTIONS The Green’s functions gPM(x) is the solution of the singular partial differential equation ...
... GREEN’S FUNCTIONS The Green’s functions gPM(x) is the solution of the singular partial differential equation ...
The Mean-Field Limit for the Dynamics of Large Particle
... force), which may lead to buildup of concentrations in the density. Both models go by the name of “Vlasov-Poisson” equation, since V is, up to a sign, the fundamental solution of Poisson’s equation −∆x U = ρ in R3 . There are many more physical examples of mean field equations of the Vlasov type tha ...
... force), which may lead to buildup of concentrations in the density. Both models go by the name of “Vlasov-Poisson” equation, since V is, up to a sign, the fundamental solution of Poisson’s equation −∆x U = ρ in R3 . There are many more physical examples of mean field equations of the Vlasov type tha ...
coherent states in quantum mechanics
... In classical physics the properties of a certain system can be described using its position x and mass m. With these variables it is possible to determine the velocity v(=dx/dt), the momentum p(=mv) and any other dynamical variable of interest. Quantum mechanics describes the time evolution of physi ...
... In classical physics the properties of a certain system can be described using its position x and mass m. With these variables it is possible to determine the velocity v(=dx/dt), the momentum p(=mv) and any other dynamical variable of interest. Quantum mechanics describes the time evolution of physi ...
A relativistic wave equation with a local kinetic operator and an
... to the constituent masses mi by means of the substitution that will be discussed in Section 3. However, these scalar interaction operators would appear in the square roots of the relativistic energies, giving rise to very serious difficulties for the calculations, unless an approximate Taylor expans ...
... to the constituent masses mi by means of the substitution that will be discussed in Section 3. However, these scalar interaction operators would appear in the square roots of the relativistic energies, giving rise to very serious difficulties for the calculations, unless an approximate Taylor expans ...
(2)
... systems. Our focus is on surface-hopping methods4–6 where the dynamics of an ensemble of trajectories is followed to represent the coupled evolution of the quantum system and bath. Typically, the classical degrees of freedom evolve by Newton’s equations of motion on adiabatic energy surfaces; the ev ...
... systems. Our focus is on surface-hopping methods4–6 where the dynamics of an ensemble of trajectories is followed to represent the coupled evolution of the quantum system and bath. Typically, the classical degrees of freedom evolve by Newton’s equations of motion on adiabatic energy surfaces; the ev ...