*Problem 1.14 A particle of mass m is in the state V (x, t) = Ae-a[(mx²/h)+it]_ where A and a are positive real constants. (a) Find A. (b) For what potential energy function V (x) does V satisfy the Schrödinger equa- tion? (c) Calculate the expectation values of x, x², p, and p². (d) Find o, and op. Is their product consistent with the uncertainty principle?
*Problem 1.14 A particle of mass m is in the state V (x, t) = Ae-a[(mx²/h)+it]_ where A and a are positive real constants. (a) Find A. (b) For what potential energy function V (x) does V satisfy the Schrödinger equa- tion? (c) Calculate the expectation values of x, x², p, and p². (d) Find o, and op. Is their product consistent with the uncertainty principle?
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![*Problem 1.14 A particle of mass m is in the state
¥ (x, t) = Ae-al(mx² /h)+it].
where A and a are positive real constants.
(a) Find A.
(b) For what potential energy function V (x) does V satisfy the Schrödinger equa-
tion?
(c) Calculate the expectation values of x, x2,
p, and p2.
(d) Find og and op. Is their product consistent with the uncertainty principle?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3b086fdb-3976-42f1-befa-17038df34170%2F377de0b9-9c54-4ad5-a4cd-61696c640557%2Fktmz31_processed.jpeg&w=3840&q=75)
Transcribed Image Text:*Problem 1.14 A particle of mass m is in the state
¥ (x, t) = Ae-al(mx² /h)+it].
where A and a are positive real constants.
(a) Find A.
(b) For what potential energy function V (x) does V satisfy the Schrödinger equa-
tion?
(c) Calculate the expectation values of x, x2,
p, and p2.
(d) Find og and op. Is their product consistent with the uncertainty principle?
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