91Ó°ÊÓ

In order to have a definite wavelength of particle, the wave function of particle has to be purely sinusoidal in nature.

According to Heisenberg uncertainty principle, the uncertainty in position for a particle inside the finite well of width L is leads to a corresponding uncertainty in momentum $\left(\mathrm{Δ}{p}_x\right)$via relation

$$\begin{gathered} L\mathrm{Δ}{p}_xâ‰\yen \frac{h}{4\mathrm{Ï€}} \\ \mathrm{Δ}{p}_xâ‰\yen \frac{h}{4\mathrm{Ï€}L} \end{gathered}$$

As, the wave function of a particle in finite potential well is sinusoidal inside the well and exponential outside the well.

Therefore it does not form a definite wavelength of a particle inside a finite potential well.

As most of the part of wave function is confined inside the well that leads to the uncertainty of momentum of the particle.

Hence, there is neither a definite state of momentum or definite state of energy for each bound state of definite energy.