Quantum Variational Calculus by Agnieszka B. Malinowska & Delfim F. M. Torres

Author:Agnieszka B. Malinowska & Delfim F. M. Torres
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

In next examples we solve quantum variational problems using Leitmann’s direct method (see Sect. 2.5).

Example 2.33

Let , and () be fixed real numbers, and be a closed interval of such that and for some . Let and be two given real numbers, . We consider the following problem:

(2.19)

We transform problem (2.19) into the trivial problem

which has solution . For that we consider the transformation

where constants and will be chosen later. According to the above, we have

and

In order to obtain the solution to the original problem, it suffices to chose and so that

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