Measuring an Electron Spin

Classical Mechanics Level 1

A electron spin in quantum mechanics is given by the superposition state:

$\large |\Psi\rangle = \frac{i}{2} |\uparrow\rangle + \dfrac{\sqrt{3}}{2} |\downarrow\rangle.$

What is the probability of measuring the spin in the $z$ -direction to have value equal to $-\dfrac{\hbar}{2}$ ?

\frac12

\frac14

\frac34

\frac{\sqrt{3}}{2}

1 solution

Matt DeCross
May 10, 2016

The probability of measuring in the spin down state is just the square of the coefficient of the spin-down state in the superposition above, which is $3/4$ .

it said the probability of measuring the spin in the z-direction, it was not mentioned that the measuring in the spin-down state.

Sumitra Barua - 7 months, 1 week ago

The negative value of the spin written in the question indicates that it is spin-down. Understanding that connection is part of the problem. Taking the spin states to be in the "up and down" z direction is standard.

Matt DeCross - 3 months, 1 week ago

Measuring an Electron Spin

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