3n s(2x – *), find 4normalized, the normalized wave function for a 1-dimensional particle- in-a-box where the box boundaries are at x=0 and x=2n. The potential energy is zero when 0
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- A quantum mechanical particle of mass m moves in a 1D potential where a) Estimate the ground state energy of the particle. b) Sketch the wave function to the best of your ability.An electron moving in a box of length ‘a’. If Z1 is the wave function at x1 = a/4 with n=1 and Z2 at x = a/4 for n=2 find Z1/Z2Consider a particle in the n = 1 state in a one-dimensional box of length a and infinite potential at the walls where the normalized wave function is given by 2 nTX a y(x) = sin (a) Calculate the probability for finding the particle between 2 and a. (Hint: It might help if you draw a picture of the box and sketch the probability density.)
- QUESTION 7 Use the Schrödinger equation to calculate the energy of a 1-dimensional particle-in-a-box system in which the normalized wave function is 4' = e sin(6x). The box boundaries are at x=0 and x=r/3. The potential energy is zero when 0 < x <- and o outside of these boundaries. 18h? m h2 8m h2 36n2m none are correctQUESTION 6 Consider a 1-dimensional particle-in-a-box system. How long is the box in radians if the wave function is Y =sin(8x) ? 4 4л none are correct T/2 O O Oa 4. 00, -Vo, V(z) = 16a 0, Use the WKB approximation to determine the minimum value that V must have in order for this potential to allow for a bound state.