Question 109 - (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.
Answer 109 - (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.
| Is This Answer Correct ? | 1 Yes | 4 No |
Question 37 - Calculate the bubble temperature T at P = 85-kPa for a binary liquid with x(1) = 0.4. The liquid solution is ideal. The saturation pressures are Psat(1) = exp [ 14.3 - 2945 / (T + 224) ], Psat(2) = exp [ 14.2 - 2943 / (T + 209) ] where T is in degree Celsius. Please take note that x(1) + x(2) = 1. Please take note that y(1) + y(2) = 1, y(1) = [ x(1) * Psat(1) ] / P, y(2) = [ x(2) * Psat(2) ] / P, * is multiplication. P is in kPa.
QUANTUM COMPUTING - EXAMPLE 32.10 : In quantum computing, the conversion of Control Not (CNOT) gate in two input quantum bit gate could be decribed as : | 00 > --> | 00 >, | 01 > --> | 01 >, | 10 > --> | 11 >, | 11 > --> | 10 >. If | P > = 0.707 ( | 01 > - | 11 > ), find the value of CNOT | P >.
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Question - Chemical Engineering Material - In crystal material, hexagonal crystal system could form 4-digit index in certain direction of solid. For [1(-1)0] direction in the hexagonal crystal systems of particular catalyst applied in fume removal of incinerator, what is the four-digit index for this direction? Hint : The transformation equations between the 3-digit [h’k’l’] and the 4-digit [hkil] indices are : h = (1/3) (2h’ – k’); i = - (h + k); k = (1/3) (2k’ – h’); l = l’. A. [(-1)100] B. [1(-1)00] C. [(-1)000] D. [00(-1)(-1)] E. [(-1)0(-1)0]
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Question 71 - (a) The byte is the basic building block of computer data used in chemical engineering process simulation where 16 bits make a word, 4 bits make a nibble, 32 bits make a quad word and 8 bits make a byte. Then how many nibbles are there in a megabytes? (b) In computer data items, let : 1 bit - counts from 0 to 1, 8 bits - counts from 0 to 255, 16 bits - counts from 0 to A. What is the value of A? (c) In a binary system of 4 bits, if 1100 = 12, 1101 = 13, 1110 = 14, 1111 = 15, B = 16, then guess the value of B. (d) By using any form of tools, find the exact value of 2 power 64 or 2^64.
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