What Would Happen If Plank's Constant Was Increased by a Magnitude of 10^30?

[wolfmanzak]

Homework Statement

I'm curious to know what kind of macroscopic changes would happen by increasing Plank's Constant to about ħ=1.0x10-4. Assuming that the behavior of all objects on length scales smaller than 1 mm (1 millimeter) remains unchanged, I know changing Plank's constant would be very strange without changing other constants but I'm curious to know what would happen with regard to

(i) the uncertainty principle,
(ii) diffraction of particles/object through small openings (e.g., single or double slits or holes), (iii) discretization of energy levels for bound systems (e.g., the infinite square well), and
(iv) interpretation of the square of the amplitude of the wavefunction as probability density.

Homework Equations

The Attempt at a Solution

I know that this problem is somewhat strange, I'm just looking for some ideas of how to convey what would happen should Planck's constant be increased by a magnitude of about 10^30.

 

[NateD]

For (i), the uncertainty principle would become much more important in that the lower the value of Planck's constant, the greater the uncertainty associated with position and momentum. This would create a greater degree of uncertainty when it comes to predicting the behavior of particles on a macroscopic scale. For (ii), diffraction of particles/objects through small openings would become much more difficult. The diffraction pattern for any given wave would be much less pronounced and the wave may have difficulty passing through a small opening. For (iii), the discretization of energy levels for bound systems would be much more pronounced due to the lower value of Planck's constant. The spacing between energy levels would be larger and thus the transition from one energy level to the next would be more difficult. Finally, for (iv), the interpretation of the square of the amplitude of the wavefunction as probability density would still remain valid, although the probability density itself would be significantly lower due to the lower value of Planck's constant. This means that the probability of finding a particle at a certain point in space would be lower than it would be with a higher value of Planck's constant.