3) Consider a particle of mass m in a one-dimensional box of width L. Apply the variational principle to determine the best estimate for the energy of the ground state using as the trial function the linear combination $(x) = c1 f1(x) + c2 f2(x) 0 < x < L

Advanced Engineering Mathematics
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Author:Erwin Kreyszig
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3) Consider a particle of mass m in a one-dimensional box of width L. Apply the
variational principle to determine the best estimate for the energy of the ground state
using as the trial function the linear combination
$(x) = c1 f1(x) + c2 f2(x)
0 <x< L
of the basis functions fi(x) = Lx – x² and f2(x) = Lx³ – xª.
Transcribed Image Text:3) Consider a particle of mass m in a one-dimensional box of width L. Apply the variational principle to determine the best estimate for the energy of the ground state using as the trial function the linear combination $(x) = c1 f1(x) + c2 f2(x) 0 <x< L of the basis functions fi(x) = Lx – x² and f2(x) = Lx³ – xª.
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