Explain why the wave function must be finite, unambiguous, and continuous.
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Explain why the wave function must be finite, unambiguous, and continuous.
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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 PROCEDUREConsider a particle of mass m which can move freely along the x axis anywhere from x=-a/2 to x=a/2, but which is strictly prohibited from being found outside this region (technically this is the infinite square well potential). 1. Verify that the attached wavefunction is a solution of the Schrodinger's equation. Consider V=0. 2. Deduce the value of the energy E. 3. Verify the uncertainty principlePlease don't provide handwritten solution ..... Determine the normalization constant for the wavefunction for a 3-dimensional box (3 separate infinite 1-dimensional wells) of lengths a (x direction), b (y direction), and c (z direction).
- 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.Solve the problem for a quantum mechanical particle trapped in a one dimensional box of length L. This means determining the complete, normalized wave functions and the possible energies. Please use the back of this sheet if you need more room.A particle of mass m is confined within a finite square well of depth V0 and width L.Sketch this potential, together with the form of the wavefunction and probability density for a particle in the lowest energy state. Briefly outline the procedure you would follow to determine the total number of energy eigenstates that can exist within a given finite square well.