TY - CHAP

T1 - Semiclassical approximation in complex plane

AU - Khriplovich, I. B.

PY - 2008/1/11

Y1 - 2008/1/11

N2 - As is known, the semiclassical approximation applies to the solution of the Schrödinger equation - ℏ/2m d2 ψ (χ)/dχ2 + U (χ)ψ(χ) = Eψ(χ) (5.1) if the potential U(χ) changes slowly at the distances on the order of the de Broglie wavelength of the particle, i.e., at those distances where the solution ψ (χ) itself varies essentially. Equation (5.1) can be rewritten somewhat otherwise: d2ψ(χ)/dχ2 + κ2 (chi;)ψ(χ) = 0, κ2(χ = 2m/ ℏ2 [E - U(χ)]. (5.2) Now the condition of applicability of the semiclassical approximation is that κ(χ) should vary slowly at the distances on the order of 1/κ(χ). Equation (5.2) describes in fact a sufficiently wide class of phenomena, in no way confined to quantum mechanics. One such problem will be considered below.

AB - As is known, the semiclassical approximation applies to the solution of the Schrödinger equation - ℏ/2m d2 ψ (χ)/dχ2 + U (χ)ψ(χ) = Eψ(χ) (5.1) if the potential U(χ) changes slowly at the distances on the order of the de Broglie wavelength of the particle, i.e., at those distances where the solution ψ (χ) itself varies essentially. Equation (5.1) can be rewritten somewhat otherwise: d2ψ(χ)/dχ2 + κ2 (chi;)ψ(χ) = 0, κ2(χ = 2m/ ℏ2 [E - U(χ)]. (5.2) Now the condition of applicability of the semiclassical approximation is that κ(χ) should vary slowly at the distances on the order of 1/κ(χ). Equation (5.2) describes in fact a sufficiently wide class of phenomena, in no way confined to quantum mechanics. One such problem will be considered below.

UR - http://www.scopus.com/inward/record.url?scp=37749012775&partnerID=8YFLogxK

U2 - 10.1007/978-0-387-75252-5_5

DO - 10.1007/978-0-387-75252-5_5

M3 - Chapter

AN - SCOPUS:37749012775

SN - 9780387752518

T3 - Lecture Notes in Physics

SP - 53

EP - 66

BT - Theoretical Kaleidoscope

A2 - Khriplovich, I.B.

ER -