- #1
g.lemaitre
- 267
- 2
I don't see how they know this is properly normalized. None of the values are specified, not psi, a sub i, E sub i, a sub k, or p sub i.
Normalizing Data: Unknown Values
- Context: Undergrad
- Thread starter g.lemaitre
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SUMMARY
The discussion focuses on the normalization of quantum states, specifically addressing the criteria for a state to be considered "properly normalized." It emphasizes that an arbitrary quantum state can be expressed as a weighted combination of energy states, as outlined in Equation 1.29. The values of these weights, denoted as a_i, must satisfy the condition in Equation 1.31 for the state to be normalized. If the state is not normalized, it can be corrected by dividing each a_i by the total magnitude, as demonstrated in Equation 1.32, ensuring that the inner product \langle \psi | \psi \rangle equals 1.
PREREQUISITES- Understanding of quantum mechanics terminology, specifically quantum states and normalization.
- Familiarity with mathematical concepts such as weighted combinations and inner products.
- Knowledge of relevant equations, particularly Equation 1.29 and Equation 1.31.
- Ability to manipulate equations and perform normalization calculations.
- Study the implications of Equation 1.29 in quantum mechanics.
- Learn how to apply normalization techniques to various quantum states.
- Explore the significance of Equation 1.31 in determining state validity.
- Investigate the mathematical foundations of inner products in quantum theory.
Students and professionals in quantum mechanics, physicists working with quantum states, and anyone involved in theoretical physics or quantum computing.
I don't see how they know this is properly normalized. None of the values are specified, not psi, a sub i, E sub i, a sub k, or p sub i.
- #2
Chopin
- 367
- 13
They're not saying that this equation follows from anything that has been given so far. They're introducing a label, "properly normalized", which can be applied to a state if and only if the condition in 1.31 is true.
Equation 1.29 tells you that any quantum state can be thought of as a weighted combination of energy states, whose weights are given by [itex]a_i[/itex]. What they're saying is that if someone hands you some arbitrary state, you can find those values by using 1.30. If the values that you find happen to satisfy 1.31, then you can call the state a normalized state. If not, then you can't call it that. In the case of a non-normalized state, you can make it normalized by dividing every [itex]a_i[/itex] by the total magnitude, which is what they're doing in 1.32. You can check to confirm that doing this will ensure that [itex]\langle \psi | \psi \rangle = 1[/itex].
Equation 1.29 tells you that any quantum state can be thought of as a weighted combination of energy states, whose weights are given by [itex]a_i[/itex]. What they're saying is that if someone hands you some arbitrary state, you can find those values by using 1.30. If the values that you find happen to satisfy 1.31, then you can call the state a normalized state. If not, then you can't call it that. In the case of a non-normalized state, you can make it normalized by dividing every [itex]a_i[/itex] by the total magnitude, which is what they're doing in 1.32. You can check to confirm that doing this will ensure that [itex]\langle \psi | \psi \rangle = 1[/itex].
- #3
g.lemaitre
- 267
- 2
thanks for clearing that up for me
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