Create and name a generic Hamiltonian operator function;
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Q: show that the following wave function is normalized.
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Create and name a generic Hamiltonian operator function;
Create and name the potential energy function of interest;
Express the wavefunctions as functions of position and quantum number;
Use these components to evaluate the mean and variance integrals for the particle-in-a-box, again.
Note: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question specifying the one you’d like answered.
Concept used:
Quantum operators act on wavefunctions to give eigen values which are physical observables.
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- Show that the following wave function is normalized. Remember to square it first. Limits of integration go from -infinity to infinity. DO NOT SKIP ANY STEPS IN THE PROCEDUREFor the quantum harmonic oscillator in one dimension, calculate the second-order energy disturbance and the first-order eigen-state for the perturbative potentials: (in the picture)Consider an electron in a one-dimensional, infinitely-deep, square potential well of width d. The electron is in the ground state. (a) Sketch the wavefunction for the electron. Clearly indicate the position of the walls of the potential well on your sketch. (b) Briefly explain how the probability distribution for detecting the electron at a given position differs from the wavefunction.
- Plot the first three wavefunctions and the first three energies for the particle in a box of length L and infinite potential outside the box. Do these for n = 1, n = 2, and n = 3A particle is trappend in a one-dimensional well. Two of its wavefunctions are shown below. (a) Identify wether the well is finite or infinite. (b) Identify the quantum number n associated with each wavefunction; (c) Overlay a sketch of the probability density for each wavefunction. n = n =what are the possible results that may be obtained upon measuring the property lz on a particle in a particular state, if its wavefunction is known to be Ψ, which is an eigenfunction of l2 such that l2Ψ=12ℏΨ? SHOW FULL AND COMPLETE PROCEDURE IN A CLEAR AND ORDERED WAY