Write down the normalized wave functions for the first three energy levels of a particle of mass m in a one-dimensional box of width L. Assume there are equal probabilities of being in each state.
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Write down the normalized wave functions for the first three energy levels of a particle of mass m in a one-dimensional box of width L. Assume there are equal probabilities of being in each state.
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- Find the corresponding Schrödinger equation and wave function, The energy for the infinite-walled well problem of size L, The expected value of x (<x>) on the interval [0,a/4], The expected value of p (<p>) for the same interval and the probability of finding at least one particle in the same interval. Do not forget the normalization, nor the conditions at the border.For a particle in a square box of side L, at what position (or positions) is the probability density a maximum if the wavefunction has n1 = 1, n2 = 3? Also, describe the position of any node or nodes in the wavefunction.Consider the potential barrier problem as illustrated in the figure below. Considering the case where E > V0: (a) find the wave function up to a constant (that is, you don't need to compute the normalization constant) (b) Calculate the reflection coefficient of the wave function. This result is expected classically?
- 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 PROCEDUREIn this question we will consider a finite potential well in which V = −V0 in the interval −L/2 ≤ x ≤ L/2, and V = 0 everywhere else (where V0 is a positive real number). For a particle with in the range −V0 < E < 0, write and solve the time-independent Schrodinger equation in the classically allowed and classically forbidden regions. Remember to keep the wavenumbers and exponential factors in your solutions real!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.
- compute d and e please!Consider a 6-functional potential well U(x) = -V8(r - a) spaced by the distance a from an infinite potential barrier U(r) o at x < 0, as shown in the figure below. Obtain an equation for the energy level Eg of a bouud state in the well. Using this equalion, find the minimum distance ae of the well from the barrier at which the bound state in the well disappears for all a < ac. Infinite potential barrier Energy level of a bound state - E, U(z) = -V6(r – a)-show that the following wave function is normalized. Remember to square it first. Show full and complete procedure