Bra-kets and operator formalism in QM - Expectation values of momentum

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SUMMARY

The discussion focuses on the application of bra-kets and operator formalism in quantum mechanics, specifically regarding the calculation of expectation values of momentum. The participant shares their solutions to a set of homework problems, highlighting the importance of using the correct notation, such as the dagger symbol for raising operators. They emphasize that careful manipulation of operators simplifies the problems. The participant requests feedback on their solutions to ensure accuracy.

PREREQUISITES
  • Understanding of quantum mechanics concepts, particularly bra-ket notation.
  • Familiarity with operator formalism in quantum mechanics.
  • Knowledge of expectation values and their significance in quantum mechanics.
  • Proficiency in mathematical manipulation of operators and equations.
NEXT STEPS
  • Study the properties of raising and lowering operators in quantum mechanics.
  • Learn about the significance of expectation values in quantum systems.
  • Explore the mathematical techniques for manipulating bra-ket expressions.
  • Review common mistakes in operator notation and their implications in quantum calculations.
USEFUL FOR

Students of quantum mechanics, physicists working with operator formalism, and anyone seeking to deepen their understanding of expectation values in quantum systems.

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Homework Statement


sup guys!

I think I've solved this set of problems, but I was just wondering if I've done it right - I have no way to tell. I'll put all the questions and answers here - plus the stuff I used. So could you please tell me if there's any mistakes?
Here it is - using Word as always!
http://imageshack.com/a/img4/750/6i29.png


Homework Equations



http://imageshack.com/a/img266/4082/58m3.jpg

BTW - I just realized I put in the transpose symbol instead of the dagger - i meant the dagger for the raising operator!

The Attempt at a Solution


http://imageshack.com/a/img546/7347/1oty.jpg
 
Last edited by a moderator:
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My solutions are here, have a look..
 

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If you are careful with the manipulations of the operators, it's an easy problem.
 

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