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Exact solutions of time-dependent Schr\"odinger equation in presence oftime-dependent potential is defined by point transformation and separation ofvariables. Energy and Heisenberg uncertainty relation are pursued fortime-independent potential whereas average energy and Heisenberg uncertaintyrelation are defined for time-dependent potential. Forces acting on a fixedboundary wall as well as average force acting on moving boundary wall arepresented along various trajectories. For high temperature, analytical forms ofpartition function and the corresponding thermodynamic quantities are derivedfollowing the Euler-Maclaurin summation formula over a finite as well as aninfinite domain for accurate presentation. Three quantum systems are generatedwith the help of point transformation, separation of variables andsuper-symmetric quantum mechanics from one quantum system and the correspondingresults are compared among all systems, where two of them are time-independentand another two are time-dependent.

Comparison between time-independent and time-dependent quantum systems  in the context of energy, Heisenberg uncertainty, average energy, force,  average force and thermodynamic quantities