Question

Which of these are the characteristic of wave function $\psi$?
(A) $\psi$ must be single valued
(B) $\int _{-\infty }^{+\infty }\,{{\psi }^{2}}dxdydz=1$
(C) $\psi$ must be finite and continuous
(D) $\psi$ can be discrete

Answer 1

Wave function must have only one numerical value at any point of space. The first and second derivatives of this wave function are continuous and finite. The overall space of a wave function must have a finite integral.

Complete step by step solution:
In quantum physics wave-particle nature in one of the key concepts. Thus each particle has its wave function. The wave function is a function of time and position and it contains all the information about the particle. The wave function is represented as $\psi$ which is called psi.
With the help of wave function, we can also calculate the probability of finding an electron in the matter-wave. This can be done if the square of imaginary no. is done to get a real no. the solution that results in the position of the electron. Here we do the square of wave function $({{\psi }^{2}})$.
Following are the characteristic of the wave function:
- About a particle all measurable information is available
- Wave function $(\psi )$ is finite and continuous
- Wave function must be single-valued
-Three dimension probability distribution is done using the wave function
- If a particle exist it the probability of finding is 1
From the above option, all are right except (D) but in option (B) all the possibilities are covered.
$\int _{-\infty }^{+\infty }\,{{\psi }^{2}}dxdydz=1$

Thus the correct option will be (B).

Note: Wave function is continuous and finite because the wave function should have the ability to describe all the potential of a particle behaviour across any region. The single value of the wave is able to describe that there is only a single value for the probability of the system.