An electron is trapped in a one-dimensional infinite potential well that is 460 pm wide; the electron is in its ground state. What is the probability that you can detect the electron in an interval of width δx = 5.0 pm centered at x = 300 pm

1.3 The effective potential of a particle is given by: Veff(r) = 2mr? + V(r). Find the effective force corresponding to this effective potential. 1.4 A hydrogen atom has an electron radial eigenfunction given by: u0,1(r) : (ezan, Obtain the probability density of this eigenfunction. 10

In a particular semiconductor device, electrons that are accelerated through a potential of 5 V attempt to tunnel through a barrier of width 0.8 nm and height 10 V. What is the tunneling probability through the barrier If the potential is zero outside * ?the barrier 1.02 x 10-8 2.26 x 10-8 4.5 x 10-8 16.4 x 10-8 1.13 x 10-8

A particle with mass 2.5 × 10^(-27) kg and energy 4.0 eV approaches a potential barrier with a height of 2.5 eV and a width of 1.0 nm. Calculate the probability of the particle tunneling through the barrier.

An electron is trapped in a region between two infinitely high energy barriers. In the region between the barriers the potential energy of the electron is zero. The normalized wave function of the electron in the region between the walls is ψ(x) = Asin(bx), where A=0.5nm1/2 and b=1.18nm-1. What is the probability to find the electron between x = 0.99nm and x = 1.01nm.

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.

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.)

Which of the following is/are correct for the equation y(x) dx defined for a particle whose state function is y(x) (11) (iii) This equation gives the probability of the particle with the range x to X₂. This equation applies to the particle moving in any dimension. This equation defines relation between the state function and the probability with the range x; to x₂- (a) Only (1) (b) (ii) and (iii) (c) (i) and (iii) (d) (i) and (ii)

An electron is trapped in a one-dimensional infinite potential well. For what (a) higher quantum number and (b) lower quantum number is the corresponding energy difference equal to the energy of the n9 level? (c) Can a pair of adjacent levels have an energy difference equal to the energy of the n4?

Here are the properties of the GaAs quantum well in the figure. v0 = 100 ??? L = 200 Å ?∗ = 0.067 m* Find the energy values ​​of the first three levels of this well. Corresponding wave functions Draw the graph. It is assumed that the effective mass m* given for the well is also valid for barriers. please. The material of the barrier is not important here. The important thing is the V0 potential.