Conditionally solvable path integral problems

Abstract

Abstract. New classes of exactly solvable potentials are discussed within the path integral formalism. They are constructed from the hypergeometric and confluent Natanzon potentials, respectively. It is found that they allow incorporation of four free parameters, which give rise to fractional power behaviour, long-range and strongly anharmonic terms. We find six different classes of such potentials.

Bond fluctuation model of polymers in random media

“…It shows that the incorporation of random fluctuations of the average bond length into the standard description of continuum Gaussian chains leads to an effective interaction that is quadratic and nonlocal in the chain coordinates. Such interactions are among the few for which the corresponding Feynman propagator can be evaluated exactly, [22][23][24][25] and they have been used to characterize a number of different problems ͑most notably the polaron problem͒. 26 But as far as we can tell, their appearance here represents the first time they have found a realistic application in the field of polymers.…”

Bound state of solution of Dirac-Coulomb problem with spatially dependent mass

“…The Dirac equation with position dependent masshas attracted greater interest as its importance has been recognised [5][6][7][8][9][10][11][12][13][14][15]. This equation has been addressed for solvable potentials by a number of different methods [19][20][21][22][23][24][25][26][27][28][29][30]. Ciftci et al [31][32][33] recently proposed an alternative method, the asymptotic iteration method (AIM) which draws the attention of a many researchers for relativistic equations [34][35][36][37][38][39][40].…”

Exact solution of the modified Pöschl–Teller potential in the tridiagonal representation

“…Exactly solvable potentials are those for which one can determine the whole spectrum analytically for a continuous range of values of the potential parameters. Conditionally exactly solvable potentials are those for which solutions can be generated only for specific values of the potential parameters, whereas quasi‐exactly solvable potentials are those for which one can determine only part of the spectrum 5–89, 10] the group theoretical method,11] the factorization method,12, 13] and the exact quantization rule method 14] are few among the many methods.…”