  Quantum mechanics is one of the basic theories of modern physics. Here, the
famous Schr\"odinger equation and the differential operators representing
mechanical quantities in quantum mechanics are derived, just based on the
principle that the translation invariance (symmetry) of a system in Hamiltonian
mechanics should be preserved in quantum mechanics. Moreover, according to the
form of the differential operators, the commutation relation in quantum
mechanics between the generalized coordinate and the generalized momentum can
be directly obtained. We believe that the results in this paper are very useful
for understanding the physical origin of quantum mechanics.
