- #1

Haorong Wu

- 415

- 90

- Homework Statement
- Given a potential field, ##V \left ( x \right ) =

\begin{cases}

0 & x \leq 0 \\

- \frac {\alpha \hbar ^2} {m x} & x \gt 0

\end{cases}

##, where ##\alpha \gt 0## is a parameter, and a state, ## \psi _0 \left ( x \right ) ##, determine whether ##\psi_0=

\begin {cases}

0 & x \leq 0 \\

Nxe^{- \alpha x} & x \gt 0 \end{cases}

## is the ground state or not.

- Relevant Equations
- None

I guess the hard way is to solve the Schrödinger equation, but that would be exhausting.

I think the F-H theorem would not apply here. So do the Virial theorem.

Are there other theorems I forget?

I think the F-H theorem would not apply here. So do the Virial theorem.

Are there other theorems I forget?