- #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
- Thread starter g.lemaitre
- Start date
In summary, the conversation discusses the concept of normalized quantum states and how they can be identified and achieved. The equation 1.29 shows that any quantum state can be expressed as a weighted combination of energy states, and 1.30 is used to find the values of the weights. The condition in 1.31 must be satisfied for a state to be considered normalized, and if not, it can be made normalized by dividing the weights by the total magnitude as shown in 1.32. This ensures that \langle \psi | \psi \rangle = 1.
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
- 368
- 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
1. What is the purpose of normalizing data with unknown values?
The purpose of normalizing data with unknown values is to standardize the data and make it more consistent for analysis. This is important when dealing with missing or unknown values, as it helps to reduce bias and improve the accuracy of the analysis.
2. How do you handle unknown values when normalizing data?
There are a few ways to handle unknown values when normalizing data. One approach is to replace the unknown values with the mean or median of the existing data. Another option is to use a statistical model to predict the missing values. Alternatively, you can remove the rows or columns with unknown values from the dataset.
3. What are some common methods used for normalizing data with unknown values?
Some common methods used for normalizing data with unknown values include mean normalization, min-max normalization, and z-score normalization. These methods help to transform the data into a more standard format, making it easier to compare and analyze.
4. Can normalizing data with unknown values improve the accuracy of a machine learning model?
Yes, normalizing data with unknown values can improve the accuracy of a machine learning model. By standardizing the data, it reduces the impact of outliers and improves the generalizability of the model. This can lead to more accurate predictions and better performance.
5. Are there any limitations to normalizing data with unknown values?
One limitation of normalizing data with unknown values is that it can introduce bias into the analysis. This is because the missing values are being replaced or predicted, which may not accurately reflect the true data. Additionally, if there are a large number of missing values, it may not be possible to accurately normalize the data.
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