Particle in a box
A particle of mass is confined between two walls, separated by a distance The particle is in the lowest energy state (ground state), and when the separation of the walls is its energy is where is the Planck's constant.
The particle exerts a force on the walls that is trying to push the walls apart. If we change the distance between the walls, the force is changing, and it can be expressed as
What is the value of
The answer is 2.0.
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1 solution
The force is F = − d L d E where the energy is E = 8 m L 2 n h 2 and in the ground state n = 1 . Accordingly
F = 8 m h 2 2 L 3 1 = L 2 E 0 ( L L 0 ) 2
and therefore A = 2 .
Interestingly, the answer is the same for a classical (no quantum mechanics) particle, see here , although the calculation is entirely different in the two problems.