Quadratic Hamiltonians and Associated Orthogonal Polynomials

✍ Scribed by Hiroyuki Matsumoto

• Publisher: Elsevier Science
• Year: 1996
• Tongue: English
• Weight: 374 KB
• Volume: 136
• Category: Article
• ISSN: 0022-1236
• DOI: 10.1006/jfan.1996.0027

✦ Synopsis

In connection with the quadratic quantum Hamiltonians, we define and study a family of the systems of orthogonal polynomials with two variables. The family includes the usual real and the complex Hermite polynomials as special examples. Some recurrence formulae and the eigenfunction expansion for the heat kernel of the corresponding quantum Hamiltonian are shown.