Starting with the time-independent Schrodinger equation, show that = 2m.
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Starting with the time-independent Schrodinger equation, show that <p2> = 2m<E - u(x)>.
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- Consider a particle in one-dimension. In quantum mechanics, we require µ(x,t)l´ dx to be finite. Why? If this is true, we call the wavefunction admissible.Use the time-dependent Schroedinger equation to calculate the period (in seconds) of the wavefunction for a particle of mass 9.109×10−31 kg in the ground state of a box of width 1.2×10−10 m.You want to determine the possible energy observable values of a particle in a non- zero potential described by a wave function. Which of the following equations represents that process? ħ² 2m ·V² + V| y = 0 +17] 26 οψ ħ² [2²] =0 &= 04 2m – iħ√y = oy xy = 06
- Consider the 1D time-independent Schrodinger equation ħ² ď² 2m dr² with the potential where to is a parameter. (a) Show that V(x) = +V(x)] = Ev v is a solution of the Schrodinger equation. ħ² mx² sech² 1 = A sech x xo (₁)Show the relation LxL = iħL for the quantum mechanical angular momentum operator LShow that the following function Y(0,9)= sin 0 cos e eiº is the solution of Schrödinger 1 1 equation: sin 0 21 sin 0 00 Y(0,0)= EY (0,9) and find the sin 0 dp? energy, E.
- Show that ? (x,t) = A cos (kx - ?t) is not a solution to the time-dependent Schroedinger equation for a free particle [U(x) = 0].Please asapThe 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)