(10) i) Use the quantum mechanical kinetic energy operator T, to find the kinetic energy of the first 2m dx? excited state of the Particle in a Box (with n = 2). ii) Then, use the relationship of kinetic energy and momentum (KE =p²/2m) to find an equation for the de Broglie wavelength of the particle in a one-dimensional box as a function only of the box length L and quantum number n. iii) Sketch the wavefunction in the box to verify that the expression you obtained in part ii) is correct.
(10) i) Use the quantum mechanical kinetic energy operator T, to find the kinetic energy of the first 2m dx? excited state of the Particle in a Box (with n = 2). ii) Then, use the relationship of kinetic energy and momentum (KE =p²/2m) to find an equation for the de Broglie wavelength of the particle in a one-dimensional box as a function only of the box length L and quantum number n. iii) Sketch the wavefunction in the box to verify that the expression you obtained in part ii) is correct.
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Transcribed Image Text:(10) i) Use the quantum mechanical kinetic energy operator T, =
to find the kinetic energy of the first
2m dx?
excited state of the Particle in a Box (with n = 2). ii) Then, use the relationship of kinetic energy and momentum (KE
= p?/2m) to find an equation for the de Broglie wavelength of the particle in a one-dimensional box as a function only
of the box length L and quantum number n. iii) Sketch the wavefunction in the box to verify that the expression you
obtained in part ii) is correct.
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