Question

Consider the state egin{pmatrix} 1/2\ 1/2\ 1/sqrt{2} end{pmatrix} corresponding to the angular momentum l=1 in the L_z basis of states with m =+1, 0, -1. If L_z^2 is measured in this state yielding a result 1, what is the state after the measurement? (a) egin{pmatrix} 1\ 0\ 0 end{pmatrix} (b) egin{pmatrix} 1/sqrt{3} \ 0\ sqrt{2/3} end{pmatrix} (c) egin{pmatrix} 0\ 0\ 1 end{pmatrix} (d) egin{pmatrix} 1/sqrt{2} \ 0\ 1/sqrt{2} end{pmatrix}

          Consider the state egin{pmatrix} 1/2\ 1/2\ 1/sqrt{2} end{pmatrix} corresponding to the angular momentum l=1 in the L_z basis of states with m =+1, 0, -1. If L_z^2 is measured in this state yielding a result 1, what is the state after the measurement?
(a) egin{pmatrix} 1\ 0\ 0 end{pmatrix} (b) egin{pmatrix} 1/sqrt{3} \ 0\ sqrt{2/3} end{pmatrix} (c) egin{pmatrix} 0\ 0\ 1 end{pmatrix} (d) egin{pmatrix} 1/sqrt{2} \ 0\ 1/sqrt{2} end{pmatrix}

Consider the state eginpmatrix 1/2 1/2 1/sqrt2 endpmatrix corresponding to the angular momentum l=1 in the Lz basis of states with m =+1, 0, -1. If Lz^2 is measured in this state yielding a result 1, what is the state after the measurement?
(a) eginpmatrix 1 0 0 endpmatrix (b) eginpmatrix 1/sqrt3 0 sqrt2/3 endpmatrix (c) eginpmatrix 0 0 1 endpmatrix (d) eginpmatrix 1/sqrt2 0 1/sqrt2 endpmatrix

Added by Henry G.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Shu Naito

08/17/2024

Step 1

The question asks us to consider a quantum state corresponding to angular momentum \(l=1\) in a basis of states with \(m=+1, 0, -1\). When the angular momentum \(L\) is measured and yields a result of 1, we are asked to determine the state of the system after the Show more…

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Consider the state egin{pmatrix} 1/2\ 1/2\ 1/sqrt{2} end{pmatrix} corresponding to the angular momentum l=1 in the L_z basis of states with m =+1, 0, -1. If L_z^2 is measured in this state yielding a result 1, what is the state after the measurement? (a) egin{pmatrix} 1\ 0\ 0 end{pmatrix} (b) egin{pmatrix} 1/sqrt{3} \ 0\ sqrt{2/3} end{pmatrix} (c) egin{pmatrix} 0\ 0\ 1 end{pmatrix} (d) egin{pmatrix} 1/sqrt{2} \ 0\ 1/sqrt{2} end{pmatrix}