This problem concerns the one-dimensional schrödinger equation with the harmonic oscillator potential u(x) = 2m00"x2. (a) calculate as a function of the variable z the hermite polynomial function h4(z). you can check your answer by looking it up on the internet, but use the formula with the nth derivative of exp(-z) to actually calculate your answer. (b) using your answer to part b, give an expression for the state y4(x), the n 4 solution to the time- out front can just be called a (c) show that your function in part c satisfies the time-independent schrödinger equation with e- hoo. in other words, put your function from part b into the time-independent schrödinger equation with e =-hoo, and show that it works.

as we know our atmosphere or air have different levels. every level has other gasses, and every gas has another permeability. when the light comes from lower permeability to higher permeability, it changes its direction. so that means that when the light comes from the moon to the earth, it changes it's direction many more times. it basically means that the shape of the light part of the moon is changed on the earth.

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the aurora is formed when charged particles emitted from the sun during a solar flare penetrate the earth's magnetic shield and collide with atoms and molecules in our atmosphere. these collisions result in countless little bursts of light, called photons, which make up the aurora.

auroras are generated by charged solar particles hitting molecules in earth's atmosphere. this usually happens in high latitudes, because our planet’s magnetic field tends to funnel these particles toward the poles. that’s why it can be experienced in northern ohio.