Question

The Schrodinger equation for a free electron of mass m and energy E written in terms of the wave function $\psi$ is $\frac{d^2\psi }{d{x}^2}+\frac{8{\pi }^{2}mE}{h^2}\psi =0$. The dimensions of the coefficient $\psi$ of in the second term must be

• A. $\left[M^1{L}^1\right]$
• B. $\left[L^2\right]$
• C. $\left[L^{-2}\right]$
• D. $\left[M^1{L}^{-1}{T}^1\right]$

Answer 1

The correct option is C $\left[L^{-2}\right]$

By dimensional analysis the dimensions of each term in an equation must be the same. In the first term the second derivative with respect to distance x indicates the dimensions of the coefficient $\psi$ of to be $\left[L^{-2}\right]$ and hence the answer.