Question

explain the physical significance of wave function

Answer 1

Question 15535

Wave function is an element of vector space over complex field (is and element of Hilbert space, where the inner product is given by $< \psi_1|\psi_2 > = \int \psi_1^*\psi_2dq$ , where q denote coordinates).

Wave function represents the state of the system, which it describes. A self-adjoint operator with real eigenvalues which represents some physical quantity (for example, energy, linear momentum etc) acts on a wave function, and gives the value of that quantity in a given state: $A\psi_{n} = A_{n}\psi_{n}$ . For a given state, $|\psi_n|^2$ is the probability density. For example, if $\psi_{n}$ is a function of coordinates, the probability for an object which it describes being found between $q$ and $q + dq$ is $\psi_n(q)dq$ . The wave function as a probability density must be normalized: $\int |\psi|^2 dq = 1$ .