Given that the commutator $$[\hat{A}^2, \hat{B}] = [\hat{A}, \hat{B}] \hat{A} + \hat{A} [\hat{A}, \hat{B}]$$, the value of  $$\left[ x, \left[ \hat{p}_x^2, x \right] \right]$$ is

 

​The term symbol for the ground state of dinitrogen cation radical N₂⁺is

​

​For a model system of three non-interacting electrons confined in a two-dimensional square box of length L, the ground state energy in units of $$\left( \frac{h^2}{8mL^2} \right)$$ is

​

​Consider a particle on a ring that is perturbed by interacting with an applied electric field (E) with the perturbation being $$H' = \mu E \cos \phi, \text{ where } \mu$$ is the dipole moment. The energy levels correct upto first order are

​For an electron in 1s orbital of  He⁺, the average value of $$r, \langle r \rangle$$ is

​

​Let the Hamiltonian H, in one-dimension, be  ​

The commutator of H with x, [H,x], is 

The equilibrium dissociation energy of a diatomic molecule is 4.75 eV and its stretching frequency corresponds to 0.5 eV. The minimum energy required to dissociate the molecule in eV is

​

​The expectation value of p² of a particle in a cubic box of side l, having the wave function ​

​

The quantum number corresponding to the z-component of the total electronic orbital angular momentum in the nitric oxide molecule is

​

When a hydrogen atom is exposed to a perturbation V=E.z, the first order correction to the wave function comes only from the orbital

​

The commutator, 

is equivalent to

​