Question

Which of these are the characteristics of the wave function $\mathrm{\Psi }$ ?
A.$\mathrm{\Psi }$ must be single-valued
B.$\underset{-\mathrm{\infty }}{\overset{+\mathrm{\infty }}{\int }}{\mathrm{\Psi }}^{2}dxdydz=1$
C.$\mathrm{\Psi }$ must be finite and continuous
D.$\mathrm{\Psi }$ represents a standing wave

Answer 1

Hint: A wave function is a mathematical expression. It is defined as a mathematical description of the quantum state of an isolated quantum system in quantum physics. The wave function associated with a moving particle is not an observable quantity and does not have any physical meaning. It is a complex quantity and represents the probability density of the possibility of finding an electron in a particular region in a given instant of time.

Complete step by step answer:
A wave function can be obtained by using an imaginary number that is squared to get a real number solution which results in the position of the particle. Some of the properties of the wave function $\mathrm{\Psi }$ are as follows:
All measurable information about the particle is available in a wave function.
$\mathrm{\Psi }$ should be continuous and single-valued.
Energy calculations are using the Schrodinger wave equation.
Probability distribution in three dimensions is established using the wave function.
The Square of the wave function ${\mathrm{\Psi }}^2$ gives the probability of finding a particle at a particular place in the given instant of time.
The probability of finding a particle is 1 if it exists.

Looking at all the above properties, we can say that the correct answer is option A.


Note:
 The concept of wave function was first introduced by Erwin Schrodinger in the year 1925 with the help of the Schrodinger equation. The Schrodinger equation can be defined as a linear partial differential equation describing the wave function, $\mathrm{\Psi }$. Schrodinger equation is:
 $[{\displaystyle \frac{-h^2}{2m}}{\mathrm{\nabla }}^2+V(r)]\mathrm{\Psi }(r)=E\mathrm{\Psi }(r)$ , it is a time-independent equation.
M is the Mass of the particle
$\mathrm{\nabla }$ is Laplacian operator
h is Planck constant
E is constant which is equal to the energy level of the system