A solution to a completely symmetric function and a completely antisymmetric function which also satisfy the Schrodinger equation with same energy and determine what happens to the completely antisymmetric function if ψ ( r 1 , r 2 , r 3 , ... r z ) is symmetric in its first two arguments.

Question

A point particle moves in space under the influence of a force derivablefrom a generalized potential of the formU(r, v) = V (r) + σ · L,where r is the radius vector from a fixed point, L is the angular momentumabout that point, and σ is the fixed vector in space. Find the components of the force on the particle in spherical polar coordinates, on the basis of the equation for the components of the generalized force Qj: Qj = −∂U/∂qj + d/dt (∂U/∂q˙j)

Answer 1

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Chapter 5.2, Problem 5.12P

(a)

To determine

A solution to a completely symmetric function and a completely antisymmetric function which also satisfy the Schrodinger equation with same energy and determine what happens to the completely antisymmetric function if ψ(r1,r2,r3,...rz) is symmetric in its first two arguments.

(b)

To determine

Show that a completely antisymmetric spin state for Z electrons is impossible, if Z>2.

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