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A particle is in ground state of an infinite square well. Find the probabilirt of finding the particle in the interval [tex]\Delta x = 0.002L[/tex] at x=L. (since delta x is small, do not integrate)

here's what I have:

[tex]\Psi*\Psi = P(x) = \frac{2}{L} sin^2 \left(\frac{ \pi x}{L} \right) \Delta x[/tex]

[tex]P = \frac{2}{L} sin^2 \left(\frac{ \pi L}{L} \right) 0.002L [/tex]

[tex]P = 2sin^2 \left(\pi \right) 0.002 [/tex]

[tex]P=0.004[/tex]

is this the correct method?

here's what I have:

[tex]\Psi*\Psi = P(x) = \frac{2}{L} sin^2 \left(\frac{ \pi x}{L} \right) \Delta x[/tex]

[tex]P = \frac{2}{L} sin^2 \left(\frac{ \pi L}{L} \right) 0.002L [/tex]

[tex]P = 2sin^2 \left(\pi \right) 0.002 [/tex]

[tex]P=0.004[/tex]

is this the correct method?

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