consider an infinite square well with sides at x= -L/2 and x = L/2 (centered at the origin). Then the potential energy is 0 for [x] L/2 Let E be the total energy of the particle. =0 (a) Solve the one-dimensional time-independent Schrodinger equation to find y(x) in each region. (b) Apply the boundary condition that must be continuous. (c) Apply the normalization condition.
consider an infinite square well with sides at x= -L/2 and x = L/2 (centered at the origin). Then the potential energy is 0 for [x] L/2 Let E be the total energy of the particle. =0 (a) Solve the one-dimensional time-independent Schrodinger equation to find y(x) in each region. (b) Apply the boundary condition that must be continuous. (c) Apply the normalization condition.
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![consider an infinite square well with sides at x= -L/2 and x = L/2 (centered at the origin). Then the potential
energy is 0 for [x] <L/2 V(x) = ∞ for [x] > L/2 Let E be the total energy of the particle.
=0
(a) Solve the one-dimensional time-independent Schrodinger equation to find y(x) in each region.
(b) Apply the boundary condition that must be continuous.
(c) Apply the normalization condition.
(d) Find the allowed values of E.
(e) Sketch w(x) for the three lowest energy states.
(f) Compare your results for (d) and (e) to the infinite square well (with sides at x=0 and x=L)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fefc0e927-4815-4e2f-82d9-9b6b5f419d74%2Ff5fd12fc-cada-4961-b1bf-c9d0e931436e%2Fqe32e5o_processed.png&w=3840&q=75)
Transcribed Image Text:consider an infinite square well with sides at x= -L/2 and x = L/2 (centered at the origin). Then the potential
energy is 0 for [x] <L/2 V(x) = ∞ for [x] > L/2 Let E be the total energy of the particle.
=0
(a) Solve the one-dimensional time-independent Schrodinger equation to find y(x) in each region.
(b) Apply the boundary condition that must be continuous.
(c) Apply the normalization condition.
(d) Find the allowed values of E.
(e) Sketch w(x) for the three lowest energy states.
(f) Compare your results for (d) and (e) to the infinite square well (with sides at x=0 and x=L)
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Can you do parts d,e,f now?
![consider an infinite square well with sides at x= -L/2 and x = L/2 (centered at the origin). Then the potential
energy is 0 for [x] <L/2 V(x) = ∞ for [x] > L/2 Let E be the total energy of the particle.
=0
(a) Solve the one-dimensional time-independent Schrodinger equation to find y(x) in each region.
(b) Apply the boundary condition that must be continuous.
(c) Apply the normalization condition.
(d) Find the allowed values of E.
(e) Sketch w(x) for the three lowest energy states.
(f) Compare your results for (d) and (e) to the infinite square well (with sides at x=0 and x=L)](https://content.bartleby.com/qna-images/question/efc0e927-4815-4e2f-82d9-9b6b5f419d74/465de8e2-e627-4396-8592-d244fdbba1a4/s4sfda6_processed.png)
Transcribed Image Text:consider an infinite square well with sides at x= -L/2 and x = L/2 (centered at the origin). Then the potential
energy is 0 for [x] <L/2 V(x) = ∞ for [x] > L/2 Let E be the total energy of the particle.
=0
(a) Solve the one-dimensional time-independent Schrodinger equation to find y(x) in each region.
(b) Apply the boundary condition that must be continuous.
(c) Apply the normalization condition.
(d) Find the allowed values of E.
(e) Sketch w(x) for the three lowest energy states.
(f) Compare your results for (d) and (e) to the infinite square well (with sides at x=0 and x=L)
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