FISHER INFORMATION FOR THE MORSE OSCILLATOR

The results for Fisher information of the Morse oscillator have thus far been reported [8] for only the ground state of the system. We make use of the wave functions in [21] to provide a general method for computing Fisher-information values for both bound and excited states of the potential. In order to visualize the effects of anharmonicity, the results of the position- and momentum-space Fisher information for the Morse function are compared with the corresponding results for the harmonic-oscillator problem. While the harmonic-oscillator Fisher information (both position and momentum) increases monotonically with the principal quantum number, the corresponding results for the Morse oscillator first increase and then decrease. Despite that, the Fisher-based uncertainty relation holds for all values of the principal quantum number.