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Show that the wave function for a hydrogen atom in the 1s state = Ae T/(1a0) satisfies the spherically symmetric Schrödinger equation -h? [d?y/dr² + 2(dp/dr)/r]/(2m) - kee²p/r = E4 by calculating the following quantities. Idr dip 1s Express your answer in terms of A, r, and ao: d1/ dr? Express your answer in terms of A, r, and [d²1g/ dr? + 2(dp 1s/d Idr)/r] Express your answer in terms of A, r, and ao. + 1s Express your answer in terms of A, r, a, m, and h. {-h? [d²p/dr? + 2(d\ /dr)ir/(2m) - k¸e²p 1sNW 18 Express your answer in terms of h, a. and m.

Show that the wave function for a hydrogen atom in the 1s state = Ae T/(1a0) satisfies the spherically symmetric Schrödinger equation -h? [d?y/dr² + 2(dp/dr)/r]/(2m) - kee²p/r = E4 by calculating the following quantities. Idr dip 1s Express your answer in terms of A, r, and ao: d1/ dr? Express your answer in terms of A, r, and [d²1g/ dr? + 2(dp 1s/d Idr)/r] Express your answer in terms of A, r, and ao. + 1s Express your answer in terms of A, r, a, m, and h. {-h? [d²p/dr? + 2(d\ /dr)ir/(2m) - k¸e²p 1sNW 18 Express your answer in terms of h, a. and m.

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Show that the wave function for a hydrogen atom in the 1s state

 ψ1s = Ae-r/(1a0)

satisfies the spherically symmetric Schrödinger equation

-ℏ2 [d2ψ/dr2 + 2(dψ/dr)/r]/(2m) - kee2ψ/r = Eψ

by calculating the following quantities.

a) dψ1s /dr
Express your answer in terms of A, r, and a0.

b) d2ψ1s / dr2
Express your answer in terms of A, r, and a0.

c) [d2ψ1s / dr2 + 2(dψ1s /dr)/r]
Express your answer in terms of A, r, and a0.

d) -ℏ2 [d2ψ1s/dr2 + 2(dψ1s/dr)/r]/(2m) - kee2ψ1s/r
Express your answer in terms of A, r, a0 m, and ℏ.

e) {-ℏ2 [d2ψ/dr2 + 2(dψ1s/dr)/r]/(2m) - kee2ψ1s/r}/ψ1s
Express your answer in terms of ℏ, a0, and m.

Show that the wave function for a hydrogen atom in the 1s state = Ae T/(1a0) satisfies the spherically symmetric Schrödinger equation -h? [d?y/dr² + 2(dp/dr)/r]/(2m) - kee²p/r = E4 by calculating the following quantities. Idr dip 1s Express your answer in terms of A, r, and ao: d1/ dr? Express your answer in terms of A, r, and [d²1g/ dr? + 2(dp 1s/d Idr)/r] Express your answer in terms of A, r, and ao. + 1s Express your answer in terms of A, r, a, m, and h. {-h? [d²p/dr? + 2(d\ /dr)ir/(2m) - k¸e²p 1sNW 18 Express your answer in terms of h, a. and m.
Transcribed Image Text:Show that the wave function for a hydrogen atom in the 1s state = Ae T/(1a0) satisfies the spherically symmetric Schrödinger equation -h? [d?y/dr² + 2(dp/dr)/r]/(2m) - kee²p/r = E4 by calculating the following quantities. Idr dip 1s Express your answer in terms of A, r, and ao: d1/ dr? Express your answer in terms of A, r, and [d²1g/ dr? + 2(dp 1s/d Idr)/r] Express your answer in terms of A, r, and ao. + 1s Express your answer in terms of A, r, a, m, and h. {-h? [d²p/dr? + 2(d\ /dr)ir/(2m) - k¸e²p 1sNW 18 Express your answer in terms of h, a. and m.
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