WKB quantization rules for three-dimensional confinement

Abstract

Confined quantum systems have been studied by various authors over the past decades, by using various mathematical techniques. In this work, we derive the WKB quantization rules for quantum systems confined in an impenetrable spherical box of radius r0. We apply the proposed method to two systems explicitly, viz., the confined harmonic oscillator and the confined hydrogen atom. The results are found to be in reasonable agreement with those obtained by other methods. PACS No.: 03.65

SWKB quantization rules for bound states in quantum wells

“…First we give a brief outline of the SWKB method, starting from the ordinary WKB approximation. Writing the potential V (x) in terms of the superpotential W (x) [8] V…”

Complexification of three potential models — II

“…PT -symmetric quantum mechanics have generated much interest in recent years [1][2][3][4][5][6][7][8][9][10]. Few years ago, Bender and others [1,2,4,9] have looked at several complex potentials with PT symmetry and have shown that the energy eigenvalues are real when PT symmetry is unbroken, whereas they come in complex conjugate pairs when PT symmetry is spontaneously broken.…”

“…Few years ago, Bender and others [1,2,4,9] have looked at several complex potentials with PT symmetry and have shown that the energy eigenvalues are real when PT symmetry is unbroken, whereas they come in complex conjugate pairs when PT symmetry is spontaneously broken. Recently, Mostafazadeh [10] in his very noteworthy work has introduced the concept of pseudo-Hermiticity and he has pointed out that all the PT -symmetric Hamiltonians regarded so far are actually P-pseudo-Hermitian, namely PHP −1 = H † .…”