Let Y(r, t) = 4(r)etot be the wavefunction of a free particle of mass m, harmonically oscillating in time. Putting W(r, t) into the Schrödinger equation and eliminating the exponentials, we obtain -V²µ = Eµ, 2m where E = wh. Since, in general, only certain quantized values of the energy E are allowable, this equation can be interpreted as an eigenvalue problem for the Laplacian operator. Find the eigenstates y and corresponding energy levels E for a free particle, enclosed in a rectangular box with edge lengths a, b, and c. Assume that the wave function vanishes at the box faces.
Let Y(r, t) = 4(r)etot be the wavefunction of a free particle of mass m, harmonically oscillating in time. Putting W(r, t) into the Schrödinger equation and eliminating the exponentials, we obtain -V²µ = Eµ, 2m where E = wh. Since, in general, only certain quantized values of the energy E are allowable, this equation can be interpreted as an eigenvalue problem for the Laplacian operator. Find the eigenstates y and corresponding energy levels E for a free particle, enclosed in a rectangular box with edge lengths a, b, and c. Assume that the wave function vanishes at the box faces.
Related questions
Question
I need the answer as soon as possible
Transcribed Image Text:Let Y(r, t) = Þ(r)et@t be the wavefunction of a free particle of mass m, harmonically oscillating in
time. Putting Y(r, t) into the Schrödinger equation and eliminating the exponentials, we obtain
V² = E4,
2m
where E = wh. Since, in general, only certain quantized values of the energy E are allowable, this equation can be
interpreted as an eigenvalue problem for the Laplacian operator. Find the eigenstates y and corresponding energy levels E
for a free particle, enclosed in a rectangular box with edge lengths a, b, and c. Assume that the wave function vanishes at
the box faces.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 5 steps with 11 images
