TY - JOUR
T1 - Various variational approximations of quantum dynamics
AU - Lasser, Caroline
AU - Su, Chunmei
N1 - Publisher Copyright:
© 2022 Author(s).
PY - 2022/7/1
Y1 - 2022/7/1
N2 - We investigate variational principles for the approximation of quantum dynamics that apply for approximation manifolds that do not have complex linear tangent spaces. The first one, dating back to McLachlan [Mol. Phys. 8, 39-44 (1964)], minimizes the residuum of the time-dependent Schrödinger equation, while the second one, originating from the lecture notes of Kramer and Saraceno [Geometry of the Time-Dependent Variational Principle in Quantum Mechanics, Lecture Notes in Physics Vol. 140 (Springer, Berlin, 1981)], imposes the stationarity of an action functional. We characterize both principles in terms of metric and symplectic orthogonality conditions, consider their conservation properties, and derive an elementary a posteriori error estimate. As an application, we revisit the time-dependent Hartree approximation and frozen Gaussian wave packets.
AB - We investigate variational principles for the approximation of quantum dynamics that apply for approximation manifolds that do not have complex linear tangent spaces. The first one, dating back to McLachlan [Mol. Phys. 8, 39-44 (1964)], minimizes the residuum of the time-dependent Schrödinger equation, while the second one, originating from the lecture notes of Kramer and Saraceno [Geometry of the Time-Dependent Variational Principle in Quantum Mechanics, Lecture Notes in Physics Vol. 140 (Springer, Berlin, 1981)], imposes the stationarity of an action functional. We characterize both principles in terms of metric and symplectic orthogonality conditions, consider their conservation properties, and derive an elementary a posteriori error estimate. As an application, we revisit the time-dependent Hartree approximation and frozen Gaussian wave packets.
UR - http://www.scopus.com/inward/record.url?scp=85135004496&partnerID=8YFLogxK
U2 - 10.1063/5.0088265
DO - 10.1063/5.0088265
M3 - Article
AN - SCOPUS:85135004496
SN - 0022-2488
VL - 63
JO - Journal of Mathematical Physics
JF - Journal of Mathematical Physics
IS - 7
M1 - 072107
ER -