The wave function of a particle moving in a one-dimensional time independent potential V(x) is given by $$\psi \left( x \right) = {e^{ - iax + b}},$$ where a and b are constants. This means that the potential V(x) is of the form
The Hamiltonian of a particle is given by $$H = \frac{{{p^2}}}{{2m}} + V\left( {\left| {\overrightarrow {\bf{r}} } \right|} \right) + \phi \left( { + \left| {\overrightarrow {\bf{r}} } \right|} \right)\overrightarrow {\bf{L}} .\overrightarrow {\bf{S}} ,$$ where $$\overrightarrow {\bf{S}} $$ is the spin, $$V\left( {\left| {\overrightarrow {\bf{r}} } \right|} \right)$$ and $$\phi \left( {\left| {\overrightarrow {\bf{r}} } \right|} \right)$$ are potential functions and $$\overrightarrow {\bf{L}} \left( { = \overrightarrow {\bf{r}} \times \overrightarrow {\bf{p}} } \right)$$ is the angular momentum. The Hamiltonian does not commute with
The radial wave function of the electrons in the state of n = 1 and 1 = 0 in hydrogen atom is \[{R_{10}} = \frac{2}{{{\text{a}}_0^{\frac{3}{2}}}}\exp \left( { - \frac{r}{{{{\text{a}}_0}}}} \right),{\text{ }}{{\text{a}}_0}\] is the Bohr radius. The most probable value of r for an electron is
