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New state dependent uncertainty principle and design of objective function for optimisation: utility of kinetic and potential energy uncertainties. (English) Zbl 1310.81100
Summary: In this work a new state dependent uncertainty principle between kinetic and potential energy is formulated using time independent Schrödinger equation and correspondence principle. Validity of the above said uncertainty principle is also demonstrated by linear variational calculation of a one-dimensional model potential. An objective function is also been designed, to support excited state non-linear variational description of bound stationary state of any type of system. This newly designed function will serve as an alternative of $$\Delta H$$ in excited state nonlinear variational purpose. The utility of these objective functions is demonstrated by already evolved non-linear variational technique by using a one-dimensional model potential where crux of the problem lies on the determination of the node of excited states.

##### MSC:
 81S05 Commutation relations and statistics as related to quantum mechanics (general)
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