ch39-p049 - 49. (a) 210 is real. Squaring it, we obtain the...

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24 22 / 2 2 / 2 21 1 21 1 55 ( ) | | (4 ) sin (4 ) sin . 16 ra rr Pr r e r e aa ψ πθ π θ −− ±± ⎛⎞ == = ⎜⎟ 64π ⎝⎠ (c) The total probability density for the three states is the sum: ( ) 222 2 210 21 1 21 1 210 21 1 21 1 44 /2 2 2 / () () | | | ) 11 cos sin sin . 8 PrP rP r r ee ψψ θθθ +− + ++= + + ⎡⎤ =+ + = ⎢⎥ 8 ⎣⎦ The trigonometric identity cos 2 + sin 2 = 1 is used. We note that the total probability density does not depend on or φ ; it is spherically symmetric. 49. (a) 210 is real. Squaring it, we obtain the probability density: / 2 2 / 2 210 210 ( ) | | (4 ) cos (4 ) cos . 32 r e r e = π8 (b) Each of the other functions is multiplied by its complex conjugate, obtained by
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This note was uploaded on 06/03/2011 for the course PHY 2049 taught by Professor Any during the Spring '08 term at University of Florida.

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