Answer to Question #101100 in Quantum Mechanics for SAHIL

Question

calculate the zero point energy of system consisting of mass of 10^ -3 kg connected to fixed point by a spring which is stretched by 10^ -2 m by a force of 10 ^ -1 N .
SYSTEM IS CONSTRAINED TO MOVE IN 1 DIRECTION.

Answer 1

The zero-point energy of system is given by formula

$E=0.5hω (1),$

where ω is the oscillator frequency, h=1.055×10^-34 J×s

We can calculate the oscillator frequency as

$ω=\sqrt{\frac{k}{m}}= \sqrt{\frac{F}{mx}} (2)$

We put (2) in (1)

$E=0.5h×(\sqrt{\frac{F}{mx}}) (3)$

In our case, we have m=10^-3 kg, x=10^-2 m, F=10^-1 N.

Using (3) we get

E=5.28×10^-33 J

Answer

5.28×10^-33 J