Page 83 - Electrical Properties of Materials

Exercises 65

where c 0 is the reciprocal of the Bohr radius [see 4.7. Show that ψ 210 as given by eqn (4.29) satisfies
eqn (4.24)]. Schrödinger’s equation. Find the corresponding energy.
Compare this energy with that obtained for the wave func-
(i) The function given by the above equation may be referred tion in the previous example. Can you draw any conclusions
to as the ψ 200 wave function. Why? from these results concerning the whole n = 2 shell?
(ii) Determine c 1 from the condition that eqn (4.32) satisfies 4.8. Solve Schrödinger’s equation for the ground state
Schrödinger’s equation. of helium neglecting the potential term between the two
(iii) Find the corresponding energy. electrons. What is the energy of the ground state calculated
(iv) Determine A from the condition that the total prob- this way? The measured value is –24.6 eV. What do you think
ability of finding the electron somewhere must be the difference is caused by? Give an explanation in physical
unity. terms.
(v) Find the most probable orbit of the electron for the wave
function of eqn (4.32) and compare your result with that 4.9. Write down the time-independent Schrödinger equation
given by the curve in Fig. 4.3 for n =2. for lithium.