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Heels 1963

[A Mathematical Theory of Scattering off Leatherwood]

Senior Lecturer; Institute For The Study of Advanced Tramping, University of British Columbia.

The Schrodinger equation of a Tramper is

mathematical equation

mgh = gravitational energy.

-1/2 K(r)2 - energy lost due to bushlawyer, mud, etc.

r = position vector of Tramper.

V(r+na) = periodic potential due to leatherwood.

n is an integer.

a = spacing of leatherwood.

Assume: mathematical equation

Solution of this equation is 1:

mathematical equation

Where U(r + na) is a function periodic in a.

mathematical equation

if only interaction between nearest neighbour leatherwoods is considered

Group velocity mathematical equation

Thus as the Tramper's wave number, k, increases he first increases his group velocity, but further increase in k causes his velocity to decrease. At a certain critical value k=2π/a he is stopped, and on further increasing k he is actually flung over backwards; i.e. undergoes Bragg reflection from the leathorwood lattice This his been experimentally verified in the case of bracken2. As k is further increased the Tramper's reverse velocity decreases, then ceases, then he starts forward again, only to be once more reflected off the leatherwood. A more detailed theory of these oscillations is given by Zener3. Superimposed on these oscillations are random scatterings off impurities, manuka, bush lawyer, other Trampers, etc., giving an entirely complex trajectory.

The Author has attempted an experimental verification of these equations on Bull Mound, but the experimental accuracy was poor due to the mist. However, the bloody page break things were impenetrable. At first night the resonance condition k = 2π/a seems impossible to satisfy since k = p/ħ-1030m-1 so λ ⋍ 10-30. Howover, Heisenberg's uncertainty principle gives Sp; δp. δx ∽M p8 ∽pλ λ∽Δ x Now it is impossible to determine a Tramper's position to better than one leatherwood tree, since any attempt to look into a leatharwood disturbs it, and hence alters the position of the entangled Trampor. Thus Δx ∽a Λ ∽ a, and the resonance condition is readily satisfied. More experimental details will be found in the literature 1,2,3

The Author would like to acknowledge the assistance of the V.U.W.T.C. in many of the preliminary experiments and in their unfailing ability to find the only patch of leather-wood for twenty miles. He would also like to thank Miss L. Redmond for many stimulating discussions". Finally he would like, to thank Mr. W.R. (Bill the Bastard) Stephenson for being 7000 miles away while this paper was being written.

Abstract: This paper shows that it is impossible to go through leatherwood at all except vanishingly small velocities.