State the Schr?dinger equation for a particle of mass m moving in the xy-plane subject to a potential energy V(x, y). What is the probability of finding it in a small area ?S centred at the point (x, y) where the wave function is ?(x, y)?

A particle of mass m is confined to a line and has a wave function ? = C exp (??² x² /2). Calculate c in terms of ? and obtain an expression for the potential energy at distance x from the origin if the total energy is h² ?²/8?²m. Write down an integral expression for the probability of finding the particle between the points x = 4 and x = 5.

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exp(-y) dy V.)