caa a22 4500 465818641 CHVBK 20180323112129.0 cr unu---uuuuu 170327e19900701xx s 000 0 eng 10.1007/BF01116547 doi (NATIONALLICENCE)springer-10.1007/BF01116547 Deal Walter Department of Chemistry, University of California, 92521, Riverside, CA, USA aut Phase-space dynamics and quantum mechanics [Elektronische Daten] [Walter Deal] Summary: Ann-dimensional system with a classical HamiltonianH(p, q, t) may be described by a phase-space distribution function D(q, p, t). The dynamical equation for D(q, p, t) is postulated to be $$\mathcal{D}(q,p,t + \delta t) = h^{ - n} \smallint \smallint e^{i2\pi S/h} \mathcal{D}*(q_0 ,p_0 ,t)dq_0 dp_0 $$ where σt is small and the phase angle 2πS/h is defined by $$S = - \Delta H\delta t + \Delta q \cdot \Delta p,$$ with $$\Delta H = H(p,q_0 ,t) - H(p_0 ,q,t);\Delta q = q - q_0 ;\Delta p = p - p_0 $$ The dynamical equation follows from a simple conceptual picture for propagation of the distribution function in phase space. This equation leads to (1) solutions of the form D(q, p, t)=h −n/2 φ* (q, t)a(p t)e i2πq · p/h where φ(q, t) anda(p, t) are related as Fourier transforms, and (2) the time-dependent Schrödinger equation. Springer-Verlag, 1990 Phase-space dynamics nationallicence Quantum theory nationallicence Schrödinger equation nationallicence Theoretica chimica acta Springer-Verlag 77/4(1990-07-01), 225-237 0040-5744 77:4<225 1990 77 214 https://doi.org/10.1007/BF01116547 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF01116547 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Deal Walter Department of Chemistry, University of California, 92521, Riverside, CA, USA aut NATIONALLICENCE 773 0- Theoretica chimica acta Springer-Verlag 77/4(1990-07-01), 225-237 0040-5744 77:4<225 1990 77 214 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer