Consider a particle moving in a one-dimensional box with walls between x=-L/3 and x=+2L/3. Find the wave-function for states with n=1 and n=2?
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- At time t = 0 a particle is described by the one-dimensional wave function 1/4 (a,0) = (²ª) e-ikre-ar² where k and a are real positive constants. Verify that the wave function (r, 0) is normalised. Hint: you may find the following standard integral useful: Loze -2² dx = √,The wave function W(x,t)=Ax^4 where A is a constant. If the particle in the box W is normalized. W(x)=Ax^4 (A x squared), for 0<=x<=1, and W(x) = 0 anywhere. A is a constant. Calculate the probability of getting a particle for the range x1 = 0 to x2 = 1/3 a. 1 × 10^-5 b. 2 × 10^-5 c. 3 × 10^-5 d. 4 × 10^-5A conduction electron is confined to a metal wire of length (1.46x10^1) cm. By treating the conduction electron as a particle confined to a one-dimensional box of the same length, find the energy spacing between the ground state and the first excited state. Give your answer in eV. Note: Your answer is assumed to be reduced to the highest power possible. Your Answer: x10 Answer
- Consider a particle moving in a one-dimensional box with walls at x = -L/2 and L/2. (a) Write the wavefunction and probability density for the state n=1. (b) If the particle has a potential barrier at x =0 to x = L/4 (where L = 10 angstroms) with a height of 10.0 eV, what would be the transmission probability of the electrons at the n = 1 state? (c) Compare the energy of the particle at the n= 1 state to the energy of the oscillator at its first excited state.For an infinite potential well of length L, determine the difference in probability that a particle might be found between x = 0.25L and x = 0.75L between the n = 3 state and the n = 5 states.Consider 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.)