Weak measurement of kinetic energy and potential energy of the quantum harmonic oscillator - Besagas, John Paul A.; Galapon, Eric A. (Quezon City Institute of Physics, College of Science, University of the Philippines Diliman, 2015)
We consider the weak measurement of the kinetic energy and potential energy of the quantum harmonic oscillator for different pre-selection states. The first case is ground state pre-selection, the second case is first excited state pre-selection and the third is nth excited state pre-selection. In three cases, the oscillator is post-selected in a gassian wave pocket whose peak is at x=xo which is far from the origin. In each of the cases, the final meter wave function is obtained in order to analyze the outcomes of the weak measurement. In each of the cases, it is found that for sufficiently large values of the meter uncertainty and post-selection parameter xo, the weak measurement may yield a negative weak value of the kinetic energy. On the other hand, the measurement of potential energy of the yields its weak value which is strictly positive. It is also found that in each of the cases, the shifts of the final meter wave function for the kinetic and potential energy measurements sum up to the energy of the harmonic oscillator corresponding to the pre-selection state. These results may provide an explanation of the likelihood that quantum harmonic oscillators can be found in the classically forbidden region.
Thesis (M.S.-Physics)--University of the Philippines Diliman
Keywords: Oscillator strengths; Quantum theory