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.
Related questions
Question
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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F17ca50f7-c8b6-4a25-b729-6432f3bb8ad3%2F009f89ad-d6f9-416f-8013-b2cf9264276d%2F6vn511h.png&w=3840&q=75)
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.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 7 steps with 8 images
