Heinsenberg UC and n=0 state?

1. Mar 13, 2006

pivoxa15

Show that by allowing the state n=0 for a particle in a 1D box will violoate the uncertainty principle, delta(x)delta(p)>=h(bar)/2

I have tried to substitute all sorts of different relationships but do seem to get anywhere. I have showed that E=0 for a ground state electron but can't seem to relate it to the uncertainty principle.

2. Mar 13, 2006

dextercioby

You just have to compute the uncertainties for each variable, x and p_{x}, knowing the wavefunction.

Daniel.

3. Mar 13, 2006

pivoxa15

If we allow n=0, the wavefunction will cease to exist hence the particle will cease to exist. Hence momentum and position of a particle does not exist or could you say 0. Hence any change in the n=0 state, the particle will continue to cease to exist. In this way the HU principle will not be satisfied. But my argument is pretty vague. Is there a quantifiable way to express this?

4. Mar 14, 2006

dextercioby

What's the energy spectrum for the particle...?

Daniel.

5. Mar 16, 2006

pivoxa15

What do you mean by the energy spectrum?

Do you mean the energy levels?
At n=0, Energy=0.
At other levels, Energy=n^2(pie)^2(hbar)^2/(2mL^2)

But how does it relate to the UC?