ISSN:
1432-2234
Keywords:
Phase-space dynamics
;
Quantum theory
;
Schrödinger equation
Source:
Springer Online Journal Archives 1860-2000
Topics:
Chemistry and Pharmacology
Notes:
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.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01116547
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