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This Demonstration considers solutions of the Schrödinger equation for a particle in a one-dimensional "infinite vee" potential: ... , setting ... for simplicity. I believe this is the first published account of this problem. The solutions of the differential equation that approach zero as ... are Airy functions ... , as can be found using ... in Mathematica. The allowed values of ... are found by requiring continuity of ... at ... . The even solutions ... require ... , which leads to ... , with ... , ... , ... , … being the first, second, third, … zeros of the Airy prime function: ... . The odd solutions ... have nodes ... , which leads to ... , with ... , ... , ... , … being the first, second, third, … zeros of the Airy function: ... . The ground state is given by ... . For user-selected ... and ... , the eigenfunctions ... , with normalization constants ... , are plotted as blue curves. The ... axis for each function coincides with the corresponding eigenvalue ... , the first ten values of which are shown on the scale at the right. The vertical scales are adjusted for optimal appearance. A checkbox lets you compare the vee-potential eigenstates with the corresponding ones of the harmonic oscillator, drawn in red. The ground states of the two systems are chosen to coincide: ... . The harmonic oscillator is more confining, so its eigenvalues are more widely spaced. For higher values of ... , the oscillator functions might move off scale.

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      EUN,LOM,LRE4,work-cmr-id:397944,http://demonstrations.wolfram.com:http://demonstrations.wolfram.com/ParticleInAnInfiniteVeePotential/,ilox,learning resource exchange,LRE metadata application profile,LRE

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