How to get from the wavefunction to weighted states?

In summary, the conversation discusses the process of arriving at probabilities for the wavefunction collapsing to a specific value for an observable. The wavefunction is a superposition of possible states depending on the observable being measured. The question asks for the procedure of obtaining possible outcomes with weighted coefficients from the wavefunction. The conversation also mentions the concept of a superposition becoming a mixed state, the Born Rule, and different resources for understanding it.
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Jarrodmccarthy
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I Have a question about how we arrive at the probabilities for the wavefunction collapsing to some specific value for an observable.

As far as I'm aware, the wavefunction is a superposition of possible states depending on the observable we try to measure.
Lets say I want to measure observable A,

What is the procedure for getting from the wavefunction to a set of possible outcomes with coefficients that weight the possibilities?

Apologies if the question isn't well formulated.
thanks in advance.
 
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1. What is a wavefunction?

A wavefunction is a mathematical description of the quantum state of a particle or system. It represents the probability amplitude of finding the particle in a specific state, and can be used to calculate the probability of obtaining a certain measurement outcome.

2. How is a wavefunction related to weighted states?

A weighted state is a specific quantum state that has been assigned a weight based on its probability amplitude in the wavefunction. The wavefunction contains all possible weighted states for a particle or system, and the weights determine the likelihood of obtaining a particular measurement outcome.

3. What is the process for obtaining weighted states from a wavefunction?

In order to obtain weighted states from a wavefunction, one must first determine the possible measurement outcomes for the particle or system. Then, the wavefunction can be used to calculate the probability amplitudes for each outcome, which can then be used to assign weights to each possible state.

4. Can weighted states be visualized?

While the wavefunction itself cannot be directly visualized, weighted states can be represented graphically as vectors with a magnitude and direction. This allows for a visual representation of the probability amplitudes and the relationship between different weighted states.

5. How does the wavefunction change over time?

The wavefunction is governed by the Schrödinger equation, which describes how the wavefunction evolves over time. As the particle or system interacts with its environment, the wavefunction will change accordingly, with the weights of the states also shifting to reflect the changing probabilities of measurement outcomes.

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