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Name:  
Miloslav Znojil  
Reviewer number:  
9689  
Email:  
znojil@ujf.cas.cz  
Item's zblNumber:  
DE 017 497 140  
Author(s):  
Casahorrán, J.  
Shorttitle:  
Quantum mechanical tunneling: Differential operators, zetafunctions and determinants.  
Source:  
Forthschr. Phys. 50, No. 3  4, 405  424 (2002).  
Classification:  
 
Primary Classification:  
 
Secondary Classification:  
 
Keywords:  
pathintegral method; double well potential; Wick rotation; instanton solutions; corrections; semiclassical technique; shape invariance; closed solutions; multiinstanton corrections.  
Review:  
A characteristic difficulty with quantization is that the related practical calculations (e.g., of Feynmann integrals) may often become prohibitively complicated (and still, mathematically, not too well founded) in the majority of the realistic phenomenological models in physics. This is the reason why the author in question picked up an oversimplified model, viz., a particle in a onedimensional double well, and applied to it a complicated universal method, viz., the evaluation of corrections to an instanton solution based on a Wick rotation in the complex plane of time. In this way one arrives at the auxiliary differential operators (of the second order), the eigenvalues and eigenfunctions of which are obtainable in closed form (construction based, by the way, on the so called shape invariance recollected in Appendix A). Then one evaluates the determinants by means of the so called zeta function method summarized briefly in Appendix B. In this way, with a patient emphasis on the key technicalities (first of all, on the zeromode removal and on the multiinstanton corrections in the dilutegas approximation), the author equips the current method with a well enhanced credit of a well deserved mathematical rigor. All done with care and pedagogical routine.  
Remarks to the editors:  