QUANTUM CHEMISTRY AND CHEMICAL ENGINEERING - EXAMPLE 31.8 : (a) Acceptable wavefunction in quantum mechanics in the range of : negative infinity < x < positive infinity, vanishes at least at one boundary. Which of the following is the wavefunction or are the wavefunctions of acceptable theory : P = x, P = | x |, P = sin x, P = exp (-x), P = exp (-| x |)? State the reason. (b) Let linear momentum operator P = -ih d / dz. The wavefunction is S = exp (-ikz) where i x i = -1, k and h are constants. Find the linear momentum of such wavefunction by using the term P x S.
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QUANTUM CHEMISTRY AND CHEMICAL ENGINEERING - ANSWER 31.8 : (a) Acceptable wavefunctions are P = sin x as the boundaries are P = +1 and -1, and P = exp (-| x |) as the boundaries are P = 1 and 0. (b) P x S = -ih d / dz [ exp (-ikz) ] = -ik x (-ih) x exp (-ikz) = -i (-i) kh x S = -kh x S. Then P = -kh = linear momentum. The answer is given by Kang Chuen Tat; PO Box 6263, Dandenong, Victoria VIC 3175, Australia; SMS +61405421706; chuentat@hotmail.com; http://kangchuentat.wordpress.com.
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