The Energy Levels and Thermodynamic Functions of the Fourth Power Oscillator

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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.