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Q8CQ

Expert-verifiedFound in: Page 278

Book edition
2nd Edition

Author(s)
Randy Harris

Pages
633 pages

ISBN
9780805303087

**Question: Section 7.5 argues that knowing all three components of would violate the uncertainty principle. Knowing its magnitude and one component does not. What about knowing its magnitude and two components? Would be left any freedom at all and if so, do you think it would be enough to satisfy the uncertainly principle? **

**Answer**

** **

Only the magnitude of L and the Z-component of L can be found accurately.

**The Uncertainty principle states that the momentum and position of a particular particle cannot be measured with great accuracy. In general, it explains that uncertainty will be there in measuring a particular variable for a specific particle.**

Write the expression for the sum of the square of the components.

${L}_{x}^{2}+{L}_{y}^{2}+{L}_{z}^{2}={\left|\text{L}\right|}^{2}$

Here, ${\left|\text{L}\right|}^{}$ is the magnitude of angular momentum vector, L_{X} is the x-component of angular momentum vector, L_{Y} is the y-component of angular momentum vector, and L_{Z }is the z-component of angular momentum vector.

It is known that L_{Z } can be known with certainty, by the equation:${L}_{Z}={m}_{l}\hslash $ , and is also quantized and can be calculated by the following equation.

$L=\sqrt{l(l+1)}\hslash $

Here, is the Plank’s Constant, and is the azimuthal quantum number

So, does not commute with L_{X} or L_{Y} . Hence, if relation is${L}_{x}^{2}+{L}_{y}^{2}+{L}_{z}^{2}={\left|\text{L}\right|}^{2}$ being used to calculate the value of L_{X} and , L_{Y} then it will be uncertain.

Thus, only the magnitude of L and the z-component of L can be found accurately.

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