Consider the wave function of a particle with mass m in an infinite potential well of width a. Quantum period (when it takes time for the wave function to return to its original state) Obtain this particle
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A: Hey dear have a look using ladder operators I solved this
Consider the wave function of a particle with mass m in an infinite potential well of width a. Quantum period (when it takes time for the wave function to return to its original state) Obtain this particle
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- The wave function for a quantum particle is given by ?(?)=??between ?=0and ?=1.00, and ?(?)=0elsewhere. Find (a) the value of the normalization constant ?, (b) the probability that the particle will be found between ?=0.300and ?=0.400, and (c) the expectation value of the particle’s position.Schrodinger equation for the special case of a constant potential energy, equal to U0. Find the general solution of Schrodinger equation when energy of particle E > U0 and when E < U0.Notice for the finite square-well potential that the wave function Ψ is not zero outside the well despite the fact that E < V0. Is it possible classically for a particle to be in a region where E < V0? Explain this result
- Suppose that in a certain system a particle free to move along one dimension (with 0 ≤ x ≤ ∞) is described by the unnormalized wavefunction Ψ(x)=e-ax with a = 2 m−1. What is the probability of finding the particle at a distance x ≥ 1 m?make a quantum scheme that performs the addition of a pair of two-qubit numbers x and y modulo 4: |x, y> → |x, x + y mod 4>The following Eigen function is a typical solution of the time-independent Schrödinger equation and satisfies boundary conditions for a particle in a confined space of a certain length. y(x) = sin (~77) (a) Plot the wave function as a function of x for L = 30 cm and n = 1, 2, 3 and 4. Note: You will need to have 4 plots in the same graph. (b) On a separate graph, plot the probability density (112) as a function of x using the conditions specified in part (a). Note: You will need to have 4 plots in the same graph. (c) Report your observations for parts (a) and (b)
- 3Calculate the average or expectation value of the position of a particle in a one-dimensional box for n=2.The figures below show the wave function describing two different states of a particle in an infinite square well. The number of nodes (within the well, but excluding the walls) in each wave function is related to the quantum number associated with the state it represents: Wave function A number of nodes = n-1 Wave function B M Determine the wavelength of the light absorbed by the particle in being excited from the state described by the wave function labelled A to the state described by the wave function labelled B. The distance between the two walls is 1.00 × 10-10 m and the mass of the particle is 1.82 × 10-30 kg. Enter the value of the wavelength in the empty box below. Your answer should be specified to an appropriate number of significant figures. wavelength = nm.