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

 ψ_1s = Ae^-r/(1a₀)

satisfies the spherically symmetric Schrödinger equation

-ℏ² [d²ψ/dr² + 2(dψ/dr)/r]/(2m) - k_ee²ψ/r = Eψ

by calculating the following quantities.

a) dψ_1s /dr
Express your answer in terms of A, r, and a₀.

b) d²ψ_1s / dr²
Express your answer in terms of A, r, and a₀.

c) [d²ψ_1s / dr² + 2(dψ_1s /dr)/r]
Express your answer in terms of A, r, and a₀.

d) -ℏ² [d²ψ_1s/dr² + 2(dψ_1s/dr)/r]/(2m) - k_ee²ψ_1s/r
Express your answer in terms of A, r, a₀ m, and ℏ.

e) {-ℏ² [d²ψ/dr² + 2(dψ_1s/dr)/r]/(2m) - k_ee²ψ_1s/r}/ψ_1s
Express your answer in terms of ℏ, a₀, and m.