Question

1. Consider a mass M moving near a flat surface (which we may take to be 0 in the presence of the gravitational acceleration g 9.8 m/s2. (a) Show using the Wilson Sommerfeld Quantization rule that the amplitude of bounces To and the system energy are quantized. For this purpose, use: / pio It may be useful to review the example of the harmonic oscillator where we used p md/dt and q-r. In the case of this question, one full cycle would be a descent from a height 20 to z = 0 with a subsequent return to = zo. Show, in particular that the quantized amplitudes and corresponding energies are 9n2h21/3 32 where 1,2.. or the set of positive integers. It may also be helpful to bear in mind kinematic formulas for a particle released from rest, namely x(t) = xo-gt2/2 and ½ = dr/dt =-gt for the downward journey where a release from rest is assumed. (b) Calculate the amplitude ro (no need in this instance to compute the energy) cor responding to the lowest lying state. Again, se mn.67 x 102 kg for the neutron mass

Answer 1

iven hat the systern eneng ie ?uanirea he Fuarlized arplitudes and casrwvespading 32 2 dl

Fence: rassx accelendion(g) 3 32n

b giVen kg MY (1.671627( 98