I am trying to formulate a solution to the particle in a box energy eigenvalue problem, without solving a differential equation, instead using eigenvectors of [itex]p^2[/itex]. My idea is to do this. Within the box (let's say it is defined between [itex][-a,a][/itex] and within this region the hamiltonian is [itex]H={p^2}/{2m}[/itex] so the solution is [itex]|\psi\rangle=c_+|p\rangle + c_- |-p\rangle [/itex]. This approach is really the free particle, but I cannot work out how to adjust the potential for the momentum representation. Any help would be appreciated.(adsbygoogle = window.adsbygoogle || []).push({});

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# Momentum space particle in a box

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