An investigation of some quantum systems using modified quantization rule form

作者：Maiz F^*

来源：Physica B: Condensed Matter , 2014, 449: 104-108.

DOI：10.1016/j.physb.2014.05.020

• Quantization rule
• Anharmonic oscillator
• Schroclinger equation
• Riccati equation
• Airy function

We propose a new simple quantization rule form: J(n) = n pi + delta(n), for exactly solvable and nonsolvable quantum systems. Here, J(n) is the momentum integral between two turning points, n the principal quantum number, and delta(n) is a function of potential parameters and n. This new quantization rule form is a generalization of the conventional one, already developed for exactly solvable quantum systems. We found that delta(n) is a constant independent of n for exactly solvable quantum systems. We carry out the expression of delta(n) for V-shape potential, and show that it takes this form delta(n) = (pi/2) + (1/a + bn +cn(2)) for anharmonic oscillators potential V(x) = alpha x(p) + beta x(2).

• 出版日期2014-9-15