The mechanical quantity is expressed by a Hermite operator is one of the basic hypotheses of quantum mechanics.All eigenvalues solved by the mechanical quantity operator eigenvalue equation are the possible values of the corresponding mechanical quantities.If one with a measuring instrument to measure the amount of value,eigenvalues can only be measured.In this paper,a Hermite matrix being similar to a diagonal matrix is proved in mathematics,and then combined with examples to explain its physical meaning.
In this chapter shows some applications of matrix and wave mechnanics. The equivalence between matrix mechanics and wave mechanics is explored in this chapter. Another approach for this equivalence is indicated as well. The Heisenberg equation of motion is applied to the quantum virial theorem and quantum theory of atoms in molecules (QTAIM) in next section. It is introduced afterwards that the Heisenberg’s matrix mechanics is applied to the helium atom leads to the concept of quantum resonance and chemical bond. Next, the use of the matrix mechanics and wave mechanics to obtain the uncertainty principle is discussed and its derivation is also given. Subsequently, Dirac’s quantum mechanics – an amalgamation of matrix mechanics and wave mechanics – is introduced. Finally, the importance of the commutation of the quantum operators to the quantum mechanics is discussed followed by some basic quantum principles from the Copenhagen interpretation. A couple of examples and exercises is also available in this chapter.(156 words).
Basic concepts of quantum mechanics: Schroedinger equation; Dirac notation; the energy representation; expectation value; Hermite operators; coherent superposition of states and motion in the quantum world; perturbation Hamiltonian. Time-dependent perturbation theory: harmonic perturbation. Transition rate: Fermi’s golden rule. The density matrix; pure and mixed states. Temporal dependence of the density operator: von Neuman equation. Randomizing Hamiltonian. Longitudinal and transverse relaxation times. Density matrix and entropy.