The Energy Levels and Thermodynamic Functions of the Fourth Power Oscillator

Abstract

The first six characteristic numbers of the reduced wave equation ψ″+(λ—ξ⁴)ψ=0 have been calculated by a method of numerical integration. These values have been compared with the corresponding values obtained from the first, second, and third Wentzel‐Kramers‐Brillouin approximations. For the fourth, fifth, and sixth characteristic numbers, the third W.K.B. approximation is correct within 0.0001. The four thermodynamic functions—(F—H₀)/RT, (H—H₀)/RT, S/R, and C/R have been calculated over the range hν₀/kT=0 to 10. A previously reported maximum in the heat capacity function, C/R, does not exist.