1. Use a Gaussian trial function () = A e bxto get an upper bound on the ground state energy for the potential V(x) = ax

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1 Use A Gaussian Trial Function A E Bxto Get An Upper Bound On The Ground State Energy For The Potential V X Ax 1 (39.01 KiB) Viewed 90 times

1. Use a Gaussian trial function () = A e bxto get an upper bound on the ground state energy for the potential V(x) = axl. 2. Now what happens if we use the potential V(x) = axt for the same w.f.? Hint: 1/3 36h'a m2 > EO (H) min h2 d2 3. Consider the Hamiltonian H 2m dx2 + mw?s? 1 2 Suppose we guessed, a trial wavefunction of the form: (x) 1 x2 + a2 Hint: The energy is 1 Ē(dmin) - Taliw And, the error made by this trial wavefunction is E(amin) - Eo EO hw/V2-hw/2 hw/2 V2-1=0.41 = 41% which is relatively large error.