Fill This Form To Receive Instant Help
Fill This Form To Receive Instant Help
Homework answers / question archive / Consider a simple one-directional quantum harmonic oscillator with Lagrangian L =1/2 mx2 —1/2mw2x2
Consider a simple one-directional quantum harmonic oscillator with Lagrangian
L =1/2 mx2 —1/2mw2x2.
a) Rewrite the trajectory as the classical trajectory (the solution of the Euler-Lagrange equations-x,;(¢)) plus the deviation from it (y(t)).So_ that the trajectory can be calculated as (x(t) = X,)(t) + y(t)). Describe in words the result obtained |
b) Given that the amplitude K (x,, t;, x;,¢;) for the particle to travel from x; at time f; to x, at time x, in the path integral formalism (the propagator) is given by the
expression:
K (2x, T|21.0) my \ Im (2 4.2) coswT — 20429]
rq, 1/21,0) = | ———_’°. exp 4 =| (2 rg) coswl — 21442
are 27ihsinwT P OhsinwT is
Generalize this expression for an arbitrary number of dimensions
