Determine the average value of Ψ2n (x) inside the well for the infi nite square-well potential for n = 1, 5, 10, and 100. Compare these averages with the classical probability of detecting the particle inside the box.

Calculate the transmission coefficient for an electron of total energy 2eV incident upon a rectangular potential barrier of height 2 eV and width 10-9 m

Consider an electron in a one-dimensional, infinitely-deep, square potential well of width d. The electron is in the ground state. (a) Sketch the wavefunction for the electron. Clearly indicate the position of the walls of the potential well on your sketch. (b) Briefly explain how the probability distribution for detecting the electron at a given position differs from the wavefunction.

The normalised wavefunction for an electron in an infinite 1D potential well of length 80 pm can be written:ψ=(0.587 ψ2)+(0.277 i ψ7)+(g ψ6). As the individual wavefunctions are orthonormal, use your knowledge to work out |g|, and hence find the expectation value for the energy of the particle, in eV.

Consider a weakly anharmonic a 1D oscillator with the poten- tial energy m U(x) = w?a² + Ba* 2 Calculate the energy levels in the first order in the small anharmonicity parameter 3 using TIPT and the ladder operators.

An electron trap in an intinite potentiad Well Electron can be considered a S free particle - having partick and energy UIS (*) sing - * २), 77 7. 7U 2. I th the pind probabilit of Kinetic 77x> write down the schrodinger eguation for the electron in infante potential well