Question

1. Let $|\Psi_1\rangle$ and $|\Psi_2\rangle$ be two orthonormal states of a physicsl system\\ $(\langle \Psi_i | \Psi_j \rangle = \delta_{ij})$, and let $\mathcal{O}$ be an observable of the system. Consider\\ the eigenvalue of $\mathcal{O}$ labeled $\lambda_n$ with the corresponding eigenstate $\phi_n$.\\ Let $P_i(\lambda_n) = |\langle \phi_n | \Psi_i \rangle|^2$\\ (a) What is the interpretation of $P_i(\lambda_n)$?\\ (b) A particle is in a state given by\\$3|\Psi_1\rangle - 4i|\Psi_1\rangle$\\ What is the probability of getting $\lambda_n$ when $\mathcal{O}$ is measured?

          1. Let $|\Psi_1\rangle$ and $|\Psi_2\rangle$ be two orthonormal states of a physicsl system\\
$(\langle \Psi_i | \Psi_j \rangle = \delta_{ij})$, and let $\mathcal{O}$ be an observable of the system. Consider\\
the eigenvalue of $\mathcal{O}$ labeled $\lambda_n$ with the corresponding eigenstate $\phi_n$.\\
Let $P_i(\lambda_n) = |\langle \phi_n | \Psi_i \rangle|^2$\\
(a) What is the interpretation of $P_i(\lambda_n)$?\\
(b) A particle is in a state given by\\$3|\Psi_1\rangle - 4i|\Psi_1\rangle$\\
What is the probability of getting $\lambda_n$ when $\mathcal{O}$ is measured?

1. Let |Ψ1⟩ and |Ψ2⟩ be two orthonormal states of a physicsl system

(⟨ | ⟩ = δij), and let 𝒪 be an observable of the system. Consider

the eigenvalue of 𝒪 labeled with the corresponding eigenstate .

Let Pi() = |⟨ | ⟩|^2

(a) What is the interpretation of Pi()?

(b) A particle is in a state given by
3|Ψ1⟩ - 4i|Ψ1⟩

What is the probability of getting when 𝒪 is measured?

Added by Diego C.

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