When electron starting from infinity combines with proton to form hydrogen atom the energy liberated is half of the potential energy lost Where does the half of the energy goes ?according to quantum mechanics electron is not moving in discrete orbits hence it cannot be used as kinetic energy of the electron

The motion is not a classical trajectory but the electron has kinetic energy.

The electron has a kinetic energy (this half you're searching for) and possibly a net momentum, depending on the orbital.

 

This results inevitably from the electron being a wave and being concentrated around the nucleus by the electric attraction. You can write the wave as a weighed sum of simpler wave functions, for instance plane waves; concentrated, or localized, implies that short waves are summed in the electron wave, and these short waves have a big momentum and energy.

 

Just because the kinetic energy increases as the electron gets smaller, the electron won't concentrate indefinitely. When the added kinetic energy cancels out the electric energy lost, the orbital is optimum and won't shrink more. This is how QM explains that matter has a volume.

 

Some orbitals (typically S orbitals) are symmetric enough that all momenta brought in the weighed sum cancel out (but kinetic energy sums up). Other orbitals (P, D, F...) are less symmetric, for instance have cylindrical symmetry, and can have a net angular momentum.

 

One trick by quantum mechanics is that wave functions are complex. By letting the phase rotate around the nucleus, but keeping the magnitude of the wave uniform along the rotation, QM achieves to give the orbital a net angular momentum without letting a "probability bump" rotate around the nucleus. So to say, the electron moves for some aspects but stands for others. This avoids the electron to radiate on such orbitals but still have an angular momentum and an orbital magnetic momentum.