Problem 2.2 Show that E must exceed the minimum value of V (x), for every normalizable solution to the time-independent Schrödinger equation. What is the classical analog to this statement? Hint: Rewrite Equation 2.5 in the form d²yr 2m = [V (x) - E]; () – E] V dx² if E < Vmin, then and its second derivative always have the same sign—argue that such a function cannot be normalized. h² d² 2m dx² + Vý= Ev. (2.5)
Problem 2.2 Show that E must exceed the minimum value of V (x), for every normalizable solution to the time-independent Schrödinger equation. What is the classical analog to this statement? Hint: Rewrite Equation 2.5 in the form d²yr 2m = [V (x) - E]; () – E] V dx² if E < Vmin, then and its second derivative always have the same sign—argue that such a function cannot be normalized. h² d² 2m dx² + Vý= Ev. (2.5)
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![Problem 2.2 Show that E must exceed the minimum value of V (x), for every
normalizable solution to the time-independent Schrödinger equation. What is the
classical analog to this statement? Hint: Rewrite Equation 2.5 in the form
d²
2m
[V(x) - E];
dx²
if E < Vmin, then and its second derivative always have the same sign-argue
that such a function cannot be normalized.
h² d²
2m dx²
+ Vy = Ev.
(2.5)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F95bfdf8f-f85c-45fa-96ca-ef34d2f765c3%2F4b422151-d58a-4576-966f-6f0f5966491a%2F6wrlpbc_processed.png&w=3840&q=75)
Transcribed Image Text:Problem 2.2 Show that E must exceed the minimum value of V (x), for every
normalizable solution to the time-independent Schrödinger equation. What is the
classical analog to this statement? Hint: Rewrite Equation 2.5 in the form
d²
2m
[V(x) - E];
dx²
if E < Vmin, then and its second derivative always have the same sign-argue
that such a function cannot be normalized.
h² d²
2m dx²
+ Vy = Ev.
(2.5)
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