3. Consider a particle in an infinite square well potential trapped between 0 < x < a. What is the energy spectrum of the particle, and specify the allowed quantum numbers. What are the normalized energy eigenstates for this particle (i.e. the solutions to the TISE)? HINT: You should have memorized this. You may derive it, but it is time consuming! The two wave functions are not solutions to the Schrodinger Equation. For each case, explain why. (nax (i) n (x, t) = e-icst (ii) n(x, t) = cos(wt) sin| cos
3. Consider a particle in an infinite square well potential trapped between 0 < x < a. What is the energy spectrum of the particle, and specify the allowed quantum numbers. What are the normalized energy eigenstates for this particle (i.e. the solutions to the TISE)? HINT: You should have memorized this. You may derive it, but it is time consuming! The two wave functions are not solutions to the Schrodinger Equation. For each case, explain why. (nax (i) n (x, t) = e-icst (ii) n(x, t) = cos(wt) sin| cos
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Transcribed Image Text:3. Consider a particle in an infinite square well potential trapped between 0 < x < a.
What is the energy spectrum of the particle, and specify the allowed quantum numbers.
What are the normalized energy eigenstates for this particle (i.e. the solutions to the TISE)?
HINT: You should have memorized this. You may derive it, but it is time consuming!
The two wave functions are not solutions to the Schrodinger Equation. For each case, explain why.
(i) yn (x, t) = e-ist cos
(ii) ý, (x, t) = cos(wt) sin
Expert Solution
Step 1
The energy eigen values of a particle confined in an infinite well with width a is given by
n is the quantum number specifying the energy level.
n=1 corresponds to ground state of the particle.
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