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This is one of the three classic particle-in-a-box problems in elementary quantum mechanics, along with the cuboid and the sphere. For a particle of mass ... in a right circular cylinder of radius ... and altitude ... , the Schrödinger equation in cylindrical coordinates ... , ... , ... can be written as ... . The equation is separable, as ... . The ... and ... factors are elementary functions: ... , with ... and ... , with ... . The equation for ... can be reduced to ... with the boundary condition ... . The solutions are Bessel functions ... such that ... is the ... zero of the Bessel function ... . The total energy is then given by ... . This Demonstration shows contour plots of the wavefunction through horizontal cross sections of the cylinder, representing constant values of ... between 0 and ... . The wavefunction is positive in the light blue regions.

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      EUN,LOM,LRE4,work-cmr-id:398049,http://demonstrations.wolfram.com:http://demonstrations.wolfram.com/QuantumMechanicalParticleInACylinder/,ilox,learning resource exchange,LRE metadata application profile,LRE

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