Sommerfeld's Quantum Condition of Action and the Spectra of Quantum Schwarzschild Black Hole

If the situation of quantum gravity nowadays is nearly the same as that of quantum mechanics in its early time of Bohr and Sommerfeld, then a first-step study of the quantum gravity under Sommerfeld's quantum condition of action might be helpful. We present the spectra of quantum Schwarzschild black hole in non-relativistic quantum mechanics. It is found that the quantum of area is 8πlp2/3, the quantum of entropy is 2πkB/3, and the Hawking evaporation will cease when the black hole reaches the ground state m = mp/(2(3)1/2).