On Lame's equation of a particular kind

Abstract

It is shown that the Lame's equation $\frac{d^2}{d{z}^2}X+{\kappa }^{2}c{n}^2(z,\frac{1}{\sqrt{2}})X=0$ can be reduced to the hyper-geometric equation. The characteristic exponents of this equation are expressed in terms of elementary functions of the parameter $\kappa$. An analytical condition for parametric amplification is obtained.

Stylistic changes, English improved and new discussion added

References in corpus (2)

• Towards the Theory of Reheating After Inflation
• Superconducting vortex avalanches, voltage bursts, and vortex plastic flow: Effect of the microscopic pinning landscape on the macroscopic properties

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