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h. 2 Review Consider a system with two different observables we can measure, hich we will denote A, and B. Measuring observable A can give two possible easurement results, a1 milarly, measuring observable B leads to an outcome of bị = +6 eV or b2 = +1 eV. le can label the eigenstate of A and B using the eigenvalues (measurement results), e. +2 eV or az = -4 eV, (eV stands for electron-Volts). Âla¡) = (+2 eV)|a1). (1) %3D uppose we do many experiments on this system and we determine the following lationship between |b2) and the eigenstates of Â: |b2) gla1) + V5i la2) (2) 3 a) Express  in diagonal matrix notation. b) Write the other 3 eigenvalue equations, similar to Eq. 1. c) Determine the state |b1) in the A basis (similar to Eq. 2). Ensure that |b1) and |b2) form an orthonormal set.

h. 2 Review Consider a system with two different observables we can measure, hich we will denote A, and B. Measuring observable A can give two possible easurement results, a1 milarly, measuring observable B leads to an outcome of bị = +6 eV or b2 = +1 eV. le can label the eigenstate of A and B using the eigenvalues (measurement results), e. +2 eV or az = -4 eV, (eV stands for electron-Volts). Âla¡) = (+2 eV)|a1). (1) %3D uppose we do many experiments on this system and we determine the following lationship between |b2) and the eigenstates of Â: |b2) gla1) + V5i la2) (2) 3 a) Express  in diagonal matrix notation. b) Write the other 3 eigenvalue equations, similar to Eq. 1. c) Determine the state |b1) in the A basis (similar to Eq. 2). Ensure that |b1) and |b2) form an orthonormal set.

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
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Ch. 2 Review Consider a system with two different observables we can measure, which we will denote A, and B. Measuring observable A can give two possible measurement results, a1 = +2 eV or az = -4 eV, (eV stands for electron-Volts). Similarly, measuring observable B leads to an outcome of bị = +6 eV or b2 = +1 eV. We can label the eigenstate of A and B using the eigenvalues (measurement results), i.e. Âlaz) = (+2 eV)\a1). (1) %3D Suppose we do many experiments on this system and we determine the following relationship between |b2) and the eigenstates of Â: |62) la1) + la2) (2) 3 (a) Express A in diagonal matrix notation. (b) Write the other 3 eigenvalue equations, similar to Eq. 1. (c) Determine the state |b1) in the A basis (similar to Eq. 2). Ensure that |b1) and |b2) form an orthonormal set. (d) Suppose a particle is prepared in the state |b2) and then sent to a measurement device to measure Ã. What are the possible measurement outcomes and what are their probabilities? (e) Suppose a particle is prepared in the state |b2). What is the expectation value of (Â)? (f) Suppose a particle is prepared in the state |b2). Without doing a calculation, what is the expectation value (B) and uncertainty AB? Explain your reason- ing.
Transcribed Image Text:Ch. 2 Review Consider a system with two different observables we can measure, which we will denote A, and B. Measuring observable A can give two possible measurement results, a1 = +2 eV or az = -4 eV, (eV stands for electron-Volts). Similarly, measuring observable B leads to an outcome of bị = +6 eV or b2 = +1 eV. We can label the eigenstate of A and B using the eigenvalues (measurement results), i.e. Âlaz) = (+2 eV)\a1). (1) %3D Suppose we do many experiments on this system and we determine the following relationship between |b2) and the eigenstates of Â: |62) la1) + la2) (2) 3 (a) Express A in diagonal matrix notation. (b) Write the other 3 eigenvalue equations, similar to Eq. 1. (c) Determine the state |b1) in the A basis (similar to Eq. 2). Ensure that |b1) and |b2) form an orthonormal set. (d) Suppose a particle is prepared in the state |b2) and then sent to a measurement device to measure Ã. What are the possible measurement outcomes and what are their probabilities? (e) Suppose a particle is prepared in the state |b2). What is the expectation value of (Â)? (f) Suppose a particle is prepared in the state |b2). Without doing a calculation, what is the expectation value (B) and uncertainty AB? Explain your reason- ing.
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