QUANTUM CHEMISTRY AND CHEMICAL ENGINEERING - EXAMPLE 31.2 : (a) Let | - > = 1 | x > + 0 | y >, | | > = 0 | x > + 1 | y >. Find the value of 2 | x > + 3 | y > in term of | - > and | | >. (b) Let m to be the reduced mass. Find the value of m in term of Ma and Mb where 1 / m = 1 / Ma + 1 / Mb.
QUANTUM CHEMISTRY AND CHEMICAL ENGINEERING - ANSWER 31.2 : (a) For | - > = 1 | x > + 0 | y >, multiply it with 2 to produce 2 | - > = 2 | x > + 0 | y >, then 2 | x > = 2 | - > - 0 | y > as first equation. For | | > = 0 | x > + 1 | y >, multiply it with 3 to produce 3 | | > = 0 | x > + 3 | y >, then 3 | y > = 3 | | > - 0 | x > as second equation. Finally first equation plus second equation to produce 2 | x > + 3 | y > = 2 | - > + 3 | | >. (b) Let 1 / m = 1 / Ma + 1 / Mb = (Ma + Mb) / (Ma x Mb). Then m = (Ma x Mb) / (Ma + Mb). 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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QUANTUM COMPUTING - EXAMPLE 32.2 : (a) If | 001 > = | 1 >, | 111 > = | 7 >, find the 2 possible values of ( | 001 > + | 1 > + | 7 > ) ( | 111 > ). (b) In quantum money, a duplicate will have probability P of passing the verification test of a bank, if the total number of photons on the bank note is N. The would be counterfeiter has a probability p of success in duplicating the quantum money correctly for each photon. Guess the relationship of P, p and N as a mathematical formula involving natural logarithm ln.
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