Using completeness relation to find <Omega>=0

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In summary, the completeness relation is a mathematical tool used in quantum mechanics to express a state vector as a linear combination of basis states, stating that the sum of all possible basis states is equal to the identity operator. It is important in finding <Omega>=0 as it allows us to accurately calculate the probability of a system being in a particular state. To find <Omega>=0, we use the completeness relation to express the state of the system in terms of basis states and then calculate the probability of the system being in the ground state. This tool can be used for any quantum system with a complete and orthonormal set of basis states, but it has limitations such as only being applicable for systems with discrete energy levels and the difficulty of determining
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ChemicalTom
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I am stuck on this Self-test 1.6 in molecular quantum mechanics by atkins and friedman.
Probably making use of the completeness relation the question is the following: Show that if <Ωf>*=-Ωf*, then <Ω>=0 for any real function f.
Anyone got a clue?
 
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Hi ChemicalTom
The self test 1.6 in the book you mentioned, is different from the problem you've posted. I'm using fourth edition... correct me if I'm wrong...

Regards
 
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In the 4th edition it's the self-test 1.9 on page 33.
 
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Hi Phoenix95 I am using the fifth editon.
 
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Related to Using completeness relation to find <Omega>=0

1. What is the completeness relation and how is it used?

The completeness relation is a mathematical tool used in quantum mechanics to express a state vector as a linear combination of basis states. It states that the sum of all possible basis states is equal to the identity operator, allowing us to express any state in terms of basis states.

2. Why is the completeness relation important in finding =0?

The completeness relation is important in finding =0 because it allows us to express the state of a quantum system in terms of a complete set of basis states. This is necessary in order to accurately calculate the probability of the system being in a particular state, which is necessary for determining =0.

3. How is the completeness relation used to find =0 in quantum mechanics?

In quantum mechanics, =0 represents the ground state or lowest energy state of a system. To find =0 using the completeness relation, we first express the state of the system in terms of basis states and then use mathematical techniques to calculate the probability of the system being in the ground state.

4. Can the completeness relation be used for any quantum system?

Yes, the completeness relation can be used for any quantum system as long as we have a set of basis states that are complete and orthonormal. This means that the basis states must span the entire state space and be mutually orthogonal, satisfying the completeness relation.

5. Are there any limitations to using the completeness relation to find =0?

While the completeness relation is a powerful tool in quantum mechanics, it does have some limitations. It can only be used for systems with discrete energy levels and does not work for continuous energy spectra. Additionally, it may be difficult to determine a complete set of basis states for complex systems.

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