ENGINEERING PHYSICS - EXAMPLE 30.4 : (a) Time evolution in Heisenberg picture, according to Ehrenfest theorem is m (d / dt) < r > = < p >, where m = mass, r = position, p = momentum of a particle. If v = velocity, prove that m < v > = < p >. (b) Lande g-factor is given by Gj = Gl [ J (J + 1) - S (S + 1) + L (L + 1) ] / [ 2J (J + 1) ] + Gs [ J (J + 1) + S (S + 1) - L (L + 1) ] / [ 2J (J + 1) ]. If Gl = 1 and under approximation of Gs = 2, prove by calculation that Gj = (3/2) + [ S (S + 1) - L (L + 1) ] / [ 2J (J + 1) ].
ENGINEERING PHYSICS - ANSWER 30.4 : (a) Let (d / dt) < r > = < v >. Substitute it into m (d / dt) < r > = < p > so that m < v > = < p >, proven by momentum = mass x velocity. (b) Gj = Gl [ J (J + 1) - S (S + 1) + L (L + 1) ] / [ 2J (J + 1) ] + Gs [ J (J + 1) + S (S + 1) - L (L + 1) ] / [ 2J (J + 1) ]. When Gl = 1 and Gs = 2, Gj = [ J (J + 1) - S (S + 1) + L (L + 1) ] / [ 2J (J + 1) ] + 2 [ J (J + 1) + S (S + 1) - L (L + 1) ] / [ 2J (J + 1) ] = [ J (J + 1) + 2J (J + 1) ] / [ 2J (J + 1) ] + [ 2S (S + 1) - 2L (L + 1) - S (S + 1) + L (L + 1) ] / [ 2J (J + 1) ] = [ 3J (J + 1) ] / [ 2J (J + 1) ] + [ S (S + 1) - L (L + 1) ] / [ 2J (J + 1) ] = (3/2) + [ S (S + 1) - L (L + 1) ] / [ 2J (J + 1) ] (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.
| Is This Answer Correct ? | 0 Yes | 0 No |
sir i am senthil B.Tech Chemical Engineer which book is refer for objective type questions?
What are the affinity laws associated with dynamics pumps?
what is designing step of heat exchanger
The power required for size reduction in crushing is???
How much will be the increment for postal assistant yearly?
QUANTUM COMPUTING - EXAMPLE 32.3 : A system of linear congruences consists of 3 equations : X ≡ 1 (mod 3), X ≡ 3 (mod 5), X ≡ 4 (mod 6). X has positive values. (a) List the values of these equations from 1 to 35. Then find the minimum value of X. (b)(i) Find the least common multiple (LCM) of b = 3, 5 and 6 where X ≡ a (mod b). (ii) If b - a has the same value of all equations above, then X + (b - a) is divisible by LCM. Find the value of minimum value of X via LCM division.
What is the most common cause of solid size segregation in bulk solid systems?
THERMODYNAMIC - EXAMPLE 10.1 : The water is superheated steam at 440 degree Celsius and 17.32 megapascals. Estimate the enthalpy of the steam above. From the steam table for water at 440 degree Celsius, enthalpy of steam, h at 18 megapascals is 3103.7 kilojoules per kilogram and at 16 megapascal is 3062.8 kilojoules per kilogram. Assume that h = mP + c where P is pressure; m and c are constants at fixed temperature with small differences in P.
which accomplishments in your present position are you proud of and why?
Question 99 - (a) The quantum number m is given by m = -s, -s + 1. If s = 0.5, find the values of m. (b) | T > = (cos T) | V > + (sin T) | H >. The V and H states form a basis for all polarizations. Let cos T = 0.8. (i) If (sin T)(sin T) + (cos T)(cos T) = 1, find the value of sin T. (ii) For | T > = a | V > + b | H >, where a x a represents the probability of | V > and b x b represents the probability of | H >. Which one is more abundant, | V > or | H >? (iii) Find the value of T without using any mathematical tools.
ACCOUNTING AND FINANCIAL ENGINEERING - EXAMPLE 34.32 : In the calculation of the total cost of production of an engineering material, a linear equation Y = MX + C could be applied. Let T = total cost, F = fixed cost, V = variable cost, Q = quantity produced, W = variable cost per unit produced. Form a linear equation that relates : (a) T, F and V; (b) V, Q and W.
Explain what are the assumptions made on conservation equation?
Civil Engineering (5086)
Mechanical Engineering (4453)
Electrical Engineering (16638)
Electronics Communications (3918)
Chemical Engineering (1095)
Aeronautical Engineering (239)
Bio Engineering (96)
Metallurgy (361)
Industrial Engineering (259)
Instrumentation (3014)
Automobile Engineering (332)
Mechatronics Engineering (97)
Marine Engineering (124)
Power Plant Engineering (172)
Textile Engineering (575)
Production Engineering (25)
Satellite Systems Engineering (106)
Engineering AllOther (1379)