p415_hwk11-1 - Spring 2017 PHYS 415 Assignment 11 Hand in this assignment at the start of the class on Friday 31 March Explain the reasoning by which

p415_hwk11-1 - Spring 2017 PHYS 415 Assignment 11 Hand in...

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Spring 2017 PHYS 415 Assignment 11 Hand in this assignment at the start of the class on Friday, 31 March. Explain the reasoning by which you arrive at your answers. The neatness, legibility and logical organization of your answers will be important in deciding your mark. Late assignments will not be accepted but your lowest assignment mark will be dropped when determining your grade for the course. 1. (4 points) In class we adopted the postulate that the translation operator ˆ T for infinitesimal translations (that is defined by ˆ T ( dx ) | x i = | x + dx i ) is given by ˆ T ( dx ) = ˆ 1 - i ¯ h ˆ p x dx where ˆ p x is the momentum operator and dx is an infinitesimal translation. Starting from this postulate we proved that [ˆ x, ˆ p x ] = i ¯ h ˆ 1. In this question you are asked to prove the converse: i.e., assume that x, ˆ p x ] = i ¯ h ˆ 1 is true and use this to prove that ( ˆ 1 - i ¯ h ˆ p x dx ) | x i = | x + dx i for infinitesimal dx . [This result means that the commutation rule [ˆ x, ˆ p x ] = i ¯ h ˆ 1 can be used instead of
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  • Summer '19
  • Physics, pˆx dx, h¯i pˆx dx

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