Bounding the Bogoliubov coefficients

Understand

While over the last century or more considerable effort has been put into the problem of finding approximate solutions for wave equations in general, and quantum mechanical problems in particular, it appears that as yet relatively little work seems to have been put into the complementary problem of establishing rigourous bounds on the exact solutions.

• We have in mind either bounds on parametric amplification and the related quantum phenomenon of particle production (as encoded in the Bogoliubov coefficients), or bounds on transmission and reflection coefficients.
• Modifying and streamlining an approach developed by one of the present authors [Phys.
• Rev.