Question

Postulates of quantum mechanics and its application

Answer 1

Postulate 1. The state of a quantum mechanical system is completely specified by a function $\Psi({\bf r}, t)$ that depends on the coordinates of the particle(s) and on time. This function, called the wave function or state function, has the important property that $\Psi^{*}({\bf r}, t)

\Psi({\bf r}, t) d\tau$ is the probability that the particle lies in the volume element $d\tau$ located at ${\bf r}$ at time $t$.

Postulate 2. To every observable in classical mechanics there corresponds a linear, Hermitian operator in quantum mechanics.

Postulate 3. In any measurement of the observable associated with operator $\hat{A}$, the only values that will ever be observed are the eigenvalues $a$, which satisfy the eigenvalue equation

Postulate 4. If a system is in a state described by a normalized wave function $\Psi$, then the average value of the observable corresponding to $\hat{A}$ is given by

Postulate 5. The wavefunction or state function of a system evolves in time according to the time-dependent Schrödinger equation

Postulate 6. The total wavefunction must be antisymmetric with respect to the interchange of all coordinates of one fermion with those of another. Electronic spin must be included in this set of coordinates.

Answer 2

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