P18.2 In this problem you will derive the commutator[lx, ly] =ihl₂.a. The angular momentum vector in three dimensions has theform l = ilx + jly + kl, where the unit vectors in the x,y, and z directions are denoted by i, j, and k. Determine lx,ly, and I by expanding the 3 × 3 cross product l = r x p.The vectors r and p are given by r = ix + jy + kz andp = ipx + jpy + kpz.b. Substitute the operators for position and momentum inyour expressions for lx and ly. Always write the positionoperator to the left of the momentum operator in a simpleproduct of the two.c. Show that [Îx, îy] = ihÎ₂.

The angular momentum in quantum mechanics is given as the cross product of distance r and linear…

P18.2 In this problem you will derive the commutator [Îx, Îy] = iħl₂. a. The angular momentum vector in three dimensions has the form l ilx + jly + kl₂ where the unit vectors in the x, y, and z directions are denoted by i, j, and k. Determine lx, ly, and I by expanding the 3 × 3 cross product 1 = r × p. The vectors r and p are given by r = ix + jy + kz and p = ipx + jpy + kpz. = b. Substitute the operators for position and momentum in your expressions for 1, and ly. Always write the position operator to the left of the momentum operator in a simple product of the two. c. Show that [Îx, Îy] = iħÎ₂.

P18.2 In this problem you will derive the commutator [Îx, Îy] = iħl₂. a. The angular momentum vector in three dimensions has the form l ilx + jly + kl₂ where the unit vectors in the x, y, and z directions are denoted by i, j, and k. Determine lx, ly, and I by expanding the 3 × 3 cross product 1 = r × p. The vectors r and p are given by r = ix + jy + kz and p = ipx + jpy + kpz. = b. Substitute the operators for position and momentum in your expressions for 1, and ly. Always write the position operator to the left of the momentum operator in a simple product of the two. c. Show that [Îx, Îy] = iħÎ₂.

Physical Chemistry

2nd Edition

ISBN:9781133958437

Author:Ball, David W. (david Warren), BAER, Tomas

Publisher:Ball, David W. (david Warren), BAER, Tomas

Chapter10: Introduction To Quantum Mechanics

Section: Chapter Questions

Problem 10.40E

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Question

P18.2 In this problem you will derive the commutator
[lx, ly] =ihl₂.
a. The angular momentum vector in three dimensions has the
form l = ilx + jly + kl, where the unit vectors in the x,
y, and z directions are denoted by i, j, and k. Determine lx,
ly, and I by expanding the 3 × 3 cross product l = r x p.
The vectors r and p are given by r = ix + jy + kz and
p = ipx + jpy + kpz.
b. Substitute the operators for position and momentum in
your expressions for lx and ly. Always write the position
operator to the left of the momentum operator in a simple
product of the two.
c. Show that [Îx, îy] = ihÎ₂.

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