2. Show that the probability density for the ground-state solution of the one-dimensional Coulomb potential energy has its maximum at x = =ao.
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- iii) Consider a 2D square potential energy well with sides L (length) containing six electrons. The potential energy is infinite at the sides and zero inside. The h? single-particle energies are given by 8mL +n), where n and ny are integers. If a seventh electron is added to the system when it is in its ground state find the least energy the additional electron can have?Q 3: What is the value of the commutator [X, Px]?7. One electron is trapped in a one-dimensional square well potential with infinitely high sides. a. If you have a probe that has a width for electron detection Ax = 0.00350L in the x direction, for the first excited state ( n =2), what is the probability that the electron is found in the probe when it is centered at x = L/4, (hint: you can use an approximation for this - you do not need to do an integral)? b. What is the average number of electrons that you would detect using the probe described in part "b." centered at x = L/4, ifthe electron is in the first excited state (n = 2) for each experiment and you repeat the experiment N, =100,000 times?
- 5a) Write down the expression for the quantized energy levels, En, of a particle of mass m in an infinite square well of width L. b) State the frequency of a photon that would be emitted from a particle transitioning from the n = 2 energy level to the n = 1 energy level of this infinite square well.An electron in its ground state is trapped in the one-dimensional Coulomb potential energy. What is the probability to find it in the region between x = 0.92a and x = 1.08ao? Additional Materials eBook
- The electron moves in an infinitely deep. potential well with a width of l=0.15 nm. a) Calculate the minimum (i.e. ground state) speed of the electron. V₁=? b) Calculate the reaction force that the electron causes when it moves back and forth and collides with the other wall of the well adiabatically (thermally insulated). F=? c) Calculate the frequency of the electron's back and forth motion. f=?125. An attractive square well potential is 55 represented by -V for r a The scattering due to this potential in low energy limit is proportional to nth power of a. Here n is (1) 2 (2) 4 (3) 5 (4) 6