Question

Problems from Phillips: roblems 1: 8; 2: 3, 5. 4. Clearly and concisely answer the following conceptual questions (5 marks each) (a) According to classical mechanics, an electron moving in an atom should be able to do so with any angular momentum whatever. According to Bohr's theory of the hydrogen atom, however, the angular m omentum is quantized to L -nh/2π. Can the correspondence principle reconcile these two statements? (b) Why does the probability density function have to be everywhere real, non- negative, and of finite and definite value?

Answer 1

4.(a) Correspondence Principles states that quantum theory's will reproduces classical theory's result only in the limit of large quantum number.Hence Correspondence Principle will reproduce result for large values of n.At low values of n classical and quantum result will be different.

4.(b) Probability density function represents the probability of finding de-broglie particle.Since an imaginary,negative and infinite Probability does not make real result Since

1. Probability have values from 0 to 1 ,where 0 Probability represents that particle is not in the given volume,hence Probability density function value cannot be -1.

2.Infinite Probability at a point will represents a fix(stationary) particle or precious position of particle (with particle velocity v=0)

then according to heisenberg uncertainty principle

Δx.Δp=h/4π when Δx =0 , Δv = infinite

which voilate heisenberg uncertainty principle .

3.It is clear from point_1 that Probability density function will have a finite and definite value.

Hence Probability of finding of a particle will be always real,positive and finite for that probability density function will have to be real,non-negative and finite.