<Dl> <Dd> P n (x, t) = (2 L sin 2 ⁡ (k n (x − x c + L 2)), x c − L / 2 <x <x c + L / 2, 0, otherwise, (\ displaystyle P_ (n) (x, t) = (\ begin (cases) (\ frac (2) (L)) \ sin ^ (2) (k_ (n) (x-x_ (c) + (\ tfrac (L) (2)))), &x_ (c) - L / 2 <x <x_ (c) + L / 2, \ \ 0, & (\ text (otherwise,)) \ end (cases))) </Dd> </Dl> <Dd> P n (x, t) = (2 L sin 2 ⁡ (k n (x − x c + L 2)), x c − L / 2 <x <x c + L / 2, 0, otherwise, (\ displaystyle P_ (n) (x, t) = (\ begin (cases) (\ frac (2) (L)) \ sin ^ (2) (k_ (n) (x-x_ (c) + (\ tfrac (L) (2)))), &x_ (c) - L / 2 <x <x_ (c) + L / 2, \ \ 0, & (\ text (otherwise,)) \ end (cases))) </Dd> <P> Thus, for any value of n greater than one, there are regions within the box for which P (x) = 0 (\ displaystyle P (x) = 0), indicating that spatial nodes exist at which the particle cannot be found . </P> <P> In quantum mechanics, the average, or expectation value of the position of a particle is given by </P>

Where would a particle in the first excited state of an infinite well most likely be found