Question A1 a) Write down the one-dimensional time-dependent Schrödinger equation for a particle of mass m described by a wavefunction (t, x) in a potential V (x). b) For energy eigenstates, the wavefunction can be written as (t, x) = f(t) v(x). For this wavefunction: (i) state the time-independent equation that must be satisfied by f(x). (ii) derive an expression for f(t), in terms of the energy of the particle E. [10 marks]
Question A1 a) Write down the one-dimensional time-dependent Schrödinger equation for a particle of mass m described by a wavefunction (t, x) in a potential V (x). b) For energy eigenstates, the wavefunction can be written as (t, x) = f(t) v(x). For this wavefunction: (i) state the time-independent equation that must be satisfied by f(x). (ii) derive an expression for f(t), in terms of the energy of the particle E. [10 marks]
College Physics
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Author:Raymond A. Serway, Chris Vuille
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Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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![Question A1
a)
Write down the one-dimensional time-dependent Schrödinger equation for a particle of
mass m described by a wavefunction (t, x) in a potential V (x).
b)
For energy eigenstates, the wavefunction can be written as
(t, x) = f(t) v(x).
For this wavefunction:
(i) state the time-independent equation that must be satisfied by f(x).
(ii) derive an expression for f(t), in terms of the energy of the particle E.
[10 marks]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6c0d52ac-ebeb-4643-8051-a3a6486fdce4%2F304a05d4-df6c-4d51-b96c-727e26a97c85%2Fwjvrz1tm_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Question A1
a)
Write down the one-dimensional time-dependent Schrödinger equation for a particle of
mass m described by a wavefunction (t, x) in a potential V (x).
b)
For energy eigenstates, the wavefunction can be written as
(t, x) = f(t) v(x).
For this wavefunction:
(i) state the time-independent equation that must be satisfied by f(x).
(ii) derive an expression for f(t), in terms of the energy of the particle E.
[10 marks]
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