Exact analytical solutions of the Hamiltonian with a squared tangent potential

Taseli H.

JOURNAL OF MATHEMATICAL CHEMISTRY, cilt.34, ss.243-251, 2003 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 34
  • Basım Tarihi: 2003
  • Doi Numarası: 10.1023/b:jomc.0000004073.17023.41
  • Dergi Adı: JOURNAL OF MATHEMATICAL CHEMISTRY
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.243-251
  • Anahtar Kelimeler: Schrodinger equation, exactly solvable Hamiltonians, cotangent and tangent potentials, hypergeometric functions
  • Orta Doğu Teknik Üniversitesi Adresli: Evet

Özet

In a very recent article (M.G. Marmorino, J. Math. Chem. 32 (2002) 303), exact ground and first-excited state eigensolutions determined by trial and error have been introduced for the one-dimensional Hamiltonian with a constant multiple of a squared cotangent potential nu(nu-1) cot(2) x on the domain x is an element of(0, pi). An explicit formula for the full spectrum was then proposed by the help of numerical experiments. In the present study, the results of Marmorino are mathematically justified and generalized by transforming the problem into an equivalent hypergeometric form.