AN "ADIABATIC INVARIANCE THEOREM" FOR LINEAR OSCILLATORY SYSTEMS OF FINITE NUMBER DEGREES OF FREEDOM

Technical Report · Mon Oct 31 04:00:00 EST 1960

OSTI ID:4197223

Lenard, A

The asymptotic behavior of a linear, oscillatory system in the limit where the coefficients vary slowly compared with the characteristic frequencies is considered. Two theorems are stated and proven rigorously. The first one concerns the asymptotic expansion at times when the coefficients do not vary. The second states the sense in which the expansion is an approximation to the exact solution. Two simple special cases, given as examples, are (1) the quantum mechanical adiabatic theorem, and (2) the adiabatic invariance theorem for the harmonic oscillator. (auth)

• Research Organization: Princeton Univ., N.J. Project Matterhorn
• NSA Number: NSA-14-004062
• OSTI ID: 4197223
• Report Number(s): TID-7582(Paper 30)
• Country of Publication: Country unknown/Code not available
• Language: English

Related Subjects

ADIABATIC INVARIANCE
CHARGED PARTICLES
CIRCUITS
FREQUENCY
MATHEMATICS
OSCILLATIONS
OSCILLATORS
PHYSICS
QUANTUM MECHANICS
THERMODYNAMICS