I) A free particle of mass in one dimension has the following wavefunction:
(, ) = (^) (), ∈ ℝ.
By imposing that (, ) satisfies the free particle Schrödinger equation, deduce
the ordinary differential equation that () must satisfy. Then, solve the latter with
the initial condition (0) = 1.

ii) At time = 0, the wavefunction of a free particle of mass in 1D reads
(, 0) = sin(2)
By noticing that sin(2) is an energy eigenstate for the free particle, find the
wavefunction (, ) which solves the Schrödinger equation with the initial condition
given above. Can (, ) be normalised?

When you turn on a battery-operated device, an electrical circuit is

He viscosities of several liquids are being compared. all the liquids are poured down a slope with equal path lengths. the liquid with the highest viscosity will

As part of your daily workout, you lie on your back and push with your feet against a platform attached to two stiff springs arranged side by side so that they are parallel to each other. when you push the platform, you compress the springs. you do an amount of work of 79.0 j when you compress the springs a distance of 0.230 m from their uncompressed length. (a) what magnitude of force must you apply to hold the platform in this position? (b)how much additional work must you do to move the platform a distance 0.230 m farther? (c) what maximum force must you apply to move the platform a distance 0.230 m farther?