By G. D'Agostini (lecture.notes, draft)

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R espectively. /J At x = 0, = 1/J = 0 A + B = O A = or - . . /J = :. kx - = iSinkx - Cos kx + i Sin kx] Applying second boundary conditions, we have At x a , 'l/J 0 :::;. n or k2 = 2 1t2 a2 8 n 2 mE n Com paring this with k2 = h2 = = n ---- En = n 2h2 . . 2 1 ) , we h ave 8 ma 2 . . 22) Thus, a s n takes on different values, k also takes o n different values. For each value o f k, a wave · function does exist. Each wave function represents a standing wave pattern, the energy of each of which is is given above .

The absolute value of 1jJ is squared and integrated over the given region of space so as to get the probability of finding a pdrticle i n the given region of space . If f [\lf[ 2 dT J l \11 1 2 And if = 1 , the probabil ity of finding the particle is certain. That is why, Max Born called these wave functions as 'probability wave functions' . /J (x , t) } d'C ;::;: 0, there is no possibility of finding the particle in the given region of space. = Ae1(kx - wtl .... /J* (x , t) = Ae-1(kx - w11 . .

Making the simplest assumption that C* relation: A. �= h = mV P = 0 we have de Brolie . . J2 meV h Then de Broglie relation takes the form: A. J2 meV . . 9) 2 . 4(a) Additional Information In non-relativistic mechanics, E;. = % mv2 is negligible compared to rest energy m0C2, when v < < C. When Ek is not negligible when compared to rest energy m0C2 in case of electron like particles, then m and E;. must be treated relativistically; Thus, m= � ~ ; E,. 9 C for an electron of definite mass, Ek < m0C2• Then .

### Bayesian Reasoning in Physics by G. D'Agostini (lecture.notes, draft)

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