# Spin-3/2 particle and degeneracy in excited state

1. Jan 28, 2015

### ShayanJ

1. The problem statement, all variables and given/known data

Consider a particle with mass m in the following 1D potential:
$V(x)=\left\{ \begin{array}{lr} mgx \ \ \ x>0 \\ \infty \ \ \ \ \ \ \ x\leq 0 \end{array} \right.$
What is its minimum energy calculated using the uncertainty relation?

2. Relevant equations

$\Delta x \Delta p \geq \frac{\hbar}{2}$

3. The attempt at a solution

My problem is, I don't know what to use for $\Delta x$! I see no length scale I can use. The only thing that came into my mind was making a constant with the dimension of length using the available constants and so I got $\alpha(\frac{\hbar^2}{gm^2})^{\frac 1 3}$(where $\alpha$ is a dimensionless constant) and this gives $\Delta p \geq \frac{1}{2\alpha} (m^2 \hbar g)^{\frac 1 3} \Rightarrow E_0=\frac{1}{8\alpha^2} (m \hbar^2 g^2)^{\frac 1 3}$.
But the problem is, this method can give any multiple of $(m \hbar^2 g^2)^{\frac 1 3}$!!!
What should I do?
Thanks

2. Jan 28, 2015

### TSny

Last edited by a moderator: May 7, 2017
3. Jan 28, 2015

### ShayanJ

Thanks man, it was very helpful.

Last edited by a moderator: May 7, 2017
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