Test3-FS01 - Phys 208 Theoretical Physics Test 3 Nov 19 2001 1(25 pts Given F x y z = xy yz z sin x a Find F at(0 1 2 b Find a unit vector in the

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Phys 208 – Theoretical Physics – Test 3 -- Nov. 19, 2001 1.(25 pts) Given . F x y z xy yz z x (,,) s i n =+ + a) Find at (0, 1, 2). r F b) Find a unit vector in the direction of most rapid increase of F at (0, 1, 2). c) Find the directional derivative of F at (0, 1, 2) in the direction . 22 $$ $ ij k +− 2.(25 pts) One of the hydrogen radial wave functions is given by , where and is the Bohr radius. Rr Nr e ra 21 21 2 0 () / = 0 < < ∞ r a 0 a) Determine the constant by normalizing this radial wave function. N 21 b) Determine the most probable value of r for this radial wave function. 3.(25 pts) Calculate the divergence of , r Ar z r r r zz (, ,) ( s in ) $ sin cos $ $ θθ θ + + 23 2 which is given in cylindrical coordinates . rz 4.(25 pts) The normalized ground and first excited state wave functions of the 1-dimensional harmonic oscillator are given by: and , ψ π 0 14 2 2 / / xe a ax = ( ) 1 2 2 2 / / xax e a ax = where a is a constant and x is defined to be between and + . These states have energies and . Consider the time-dependent wave function defined as: E 0 2 = h ω / E 1 32 = h / . [] Ψ (,) // xt iE t iE t
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This note was uploaded on 01/08/2011 for the course PHYS 208 taught by Professor J.peat during the Spring '10 term at Missouri S&T.

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Test3-FS01 - Phys 208 Theoretical Physics Test 3 Nov 19 2001 1(25 pts Given F x y z = xy yz z sin x a Find F at(0 1 2 b Find a unit vector in the

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