Wave in particle in 1 box with infinite potential energy

[td21]

Homework Statement

Q.1Why when the particle's kinetic energy is smaller, the wave has longer wavelength and higher amplitude?
Q.2 Why the length of box decrease in ground state?

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Homework Equations

The Attempt at a Solution

Q.1 wavenumber k= \frac{\sqrt{2m(U-E)}}{\hbar}, isn't it?
so KE decreases, wavenumber decreases, wavelength increases?
But isn't the amplitude just (2/L)^(1/2), from the normalization techinque?

Q.2 I really do not know why the box suddenly "contract" in the ground state.

 

[td21]

can someone tell me why the amplitude of wave is affected by kinetic energy(E-U)?