QUANTUM COMPUTING - EXAMPLE 32.7 : If | ± > = 0.707 ( | 0 > ± | 1 > ), prove that | Ψ (t = 0) > = | 0 > = 0.707 ( | + > + | - > ).
QUANTUM COMPUTING - ANSWER 32.7 : | + > = 0.707 ( | 0 > + | 1 > ), | - > = 0.707 ( | 0 > - | 1 > ), | + > + | - > = 0.707 ( | 0 > + | 1 > ) + 0.707 ( | 0 > - | 1 > ) = 0.707 ( | 0 > + | 1 > + | 0 > - | 1 > ) = 0.707 ( 2 | 0 > ). | Ψ (t = 0) > = | 0 > = [ 1 / (0.707 x 2) ] ( | + > + | - > ) = 0.707 ( | + > + | - > ) (Proven). 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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BIOPROCESS ENGINEERING - EXAMPLE 14.2 : An aqueous solution with 2.5 g of a protein dissolved in 600 cubic centimeters of a solution at 20 degree Celsius was placed in a container that has a water-permeable membrane. Water permeated through the membrane until the h - level of the solution was 0.9 cm above the pure water. (a) Calculate the absolute temperature of the solution, T in Kelvin, where T (Kelvin) = T (degree Celsius) + 273.15. (b) Calculate the osmotic pressure, P of the solution by using the formula P = hrg where h is level of the solution, r is density of water with 1000 kg per cubic meter, g = 9.81 N / kg as gravitational acceleration. (c) Calculate the concentration of the protein solution, C in kg / cubic meter. (d) Calculate the molecular weight of the protein, (MW) = CRT / P where R = 8.314 Pa cubic meter / (mol K) as ideal gas constant.
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QUANTUM COMPUTING - EXAMPLE 32.6 : (a) Let H | 0 > = 0.707 ( | 0 > + | 1 > ), H | 1 > = 0.707 ( | 0 > - | 1 > ). Find the values for H | 0 > + H | 1 > and H | 0 > - H | 1 >. (b) In quantum computing, a qubyte is a quantum byte, or 8 quantum bits, a sequence processed as a unit. A qubit is a quantum bit. According to Alexander Holevo in his theorem, n qubits cannot carry more than n classical bits of information. What is the maximum amount of classical bits of information that can be carried by 1 qubyte.
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CHEMICAL FLUID MECHANIC - EXAMPLE 3.2 : The terminal velocity of a falling object, v is given by v = sqrt [ 4g (R - r) D / (3Cr) ] where sqrt is the square root of, g = 9.81, D = 0.000208, R = 1800, r = 994.6, m = 0.000893. The Reynold number, L is given by L = rD (v) / m. The C for various conditions are : C = 24 / L for L < 0.1; C = 24 (1 + 0.14 L^0.7) / L for 0.1 <= L <= 1000; C = 0.44 for 1000 < L <= 350000; C = 0.19 - 80000 / L for 350000 < L. Find the value of v for the situation above by trial and error, ^ is power, <= is less than or equal to.
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