Unformatted text preview: not even suspected for the massive particles in 1911. 039 qfull 00600 2 3 0 moderate math: complex numbers Extra keywords: (HRW977:66E) 3. A complex number z is de²ned by z = x + iy , where x and y are real numbers and i = √ − 1 is imaginary. The real part of z is x = Re[ z ] and the imaginary part is y = Im[ z ] The complex conjugate of z is de²ned by z ∗ = x − iy . a) What is zz ∗ ? b) Prove that ( z 1 z 2 ) ∗ = z ∗ 1 z ∗ 2 . c) Prove that p 1 z P ∗ = 1 z ∗ . d) Prove that p z 1 z 2 P ∗ = z ∗ 1 z ∗ 2 . 039 qfull 00700 2 5 0 moderate thinking: Schr¨odinger eqn. 4. Do the following. a) Verify that the full timedependent wave function Ψ( x,t ) = ψ ( x ) e − iEt/h − reduces the full timedependent Schr¨odinger equation − h − 2 2 m ∂ 2 Ψ ∂x 2 + V ( x )Ψ = ih − ∂ Ψ ∂t to the timeindependent Schr¨odinger equation − h − 2 2 m ∂ 2 ψ ∂x 2 + V ( x ) ψ = Eψ...
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 Fall '06
 Buchler
 Physics, Electron, Photon, Schrodinger Equation, alpha particles, matter waves

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