Problem about measurement and probability of energy

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SUMMARY

This discussion focuses on the measurement and probability of energy in quantum mechanics, specifically addressing a homework problem involving the total energy of a system. The participant successfully solved part (a) using the concept of even and odd functions, determining that C=1/a. However, they expressed uncertainty in part (b), questioning the interpretation of 'total energy of the system' and its distinction from the expectation value. The discussion highlights the importance of eigenstates of the Hamiltonian in energy measurement.

PREREQUISITES
  • Understanding of quantum mechanics principles, particularly measurement theory
  • Familiarity with Hamiltonian operators and eigenstates
  • Knowledge of even and odd functions in mathematical contexts
  • Basic grasp of expectation values in quantum systems
NEXT STEPS
  • Study the role of Hamiltonians in quantum mechanics
  • Learn about eigenstates and their significance in energy measurements
  • Explore the concept of expectation values in quantum systems
  • Investigate the mathematical properties of even and odd functions
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Students and educators in quantum mechanics, particularly those tackling problems related to energy measurement and probability in quantum systems.

BREAD
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Homework Statement


upload_2017-3-8_0-44-27.png


Homework Equations



I solve the (a) , using even,odd function. So, C=1/a

The Attempt at a Solution



I don't know how to approach (b).
I think that 'total energy of the system' doesn't mean expectation value, how can i get
total energy and probability of them?
 
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BREAD said:
I don't know how to approach (b).
I think that 'total energy of the system' doesn't mean expectation value, how can i get
total energy and probability of them?
If you measure the energy, the system can only be found in one of the eigenstates of the Hamiltonian.
 

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