The vibrational partition function for a molecule which can be described as a simple harmonic oscillator with fundamental frequency $$\nu $$ is given by

The wave function for a quantum mechanical particle in a one-dimensional box of length a is given by $$\psi = A\sin \frac{{\pi x}}{a}.$$   The value of A for a box of length 200 nm is

First order perturbation correction $$\Delta \varepsilon _n^{\left( 1 \right)}$$  to energy level $${\varepsilon _n}$$ of a simple harmonic oscillator due to the anharmonicity perturbation $$\gamma {x^3}$$ is given by

An electron of mass m is confined to a one-dimensional box of length b. If it makes a radiative transition from second excited state to the ground state/the frequency of the photon emitted is

In units of $$\frac{{{h^2}}}{{8m{l^2}}},$$  the energy difference between levels corresponding to 3 and 2 node eigen functions for a particle of mass m in a one-dimensional box of length $$l$$ is

The velocity of the electron in the hydrogen atom