Question

For Schrodinger Wave Equation $\nabla^{2}\psi+\frac{8\pi^{2}m}{h^{2}}(E-V)\psi=0$, an acceptable solution does NOT possess which of the following property?}

• A. must be continuous
• B. must be single valued
• C. must be finite
• D. $\int_{-\infty}^{-\infty}\psi^2~dxdydz \le 1$

Hint:

Remember the "CSF" rule: Continuous, Single-valued, and Finite!

Answer 1

The Correct Option is D

Step 1: Concept For a wave function ($\psi$) to be physically meaningful, it must satisfy specific boundary conditions known as "well-behaved" criteria.

Step 2: Meaning These criteria ensure that the probability density derived from the wave function is logically consistent.

Step 3: Analysis A valid wave function must be continuous, single-valued, and finite so that the electron cannot exist in two states at once or have infinite probability in a region. Option (D) suggests an integral $\le 1$; however, for a normalized wave function, the total probability of finding the particle in all space must be exactly equal to 1 ($\int \psi^2 d\tau = 1$).

Step 4: Conclusion The mathematical expression in option (D) as written (with mismatched limits and the inequality) does not represent a standard requirement for an acceptable solution. Final Answer: (D)