Show that the quantum mechanical probability

Assignment Help Chemistry

Reference no: EM13633551

1. The following questions regard the quantum mechanical particlein a box.
a) Explain why the n=0 solution is not allowed for the particle ina box but is allowed for the free particle. Cast your explanation in terms of the underlying physicalmeaning of the solution in both contexts. Hint: substitute n = 0 into the respectivewavefunctions.

b) Show that the normalization constant of the particle in a boxwavefunction is 2L . What would be the normalization constant if the box length were 2L?

c) Graph the wavefunction for the n = 3 solution to the particle ina box and indicate the corresponding energy.

d) Calculate the probability that a particle in the n = 3 statewill be found between x = 0 and x = L/3. Show that this value can be expected from the symmetry of thewavefunction.

e) Show that the quantum mechanical probability distributionapproaches the classical probability distribution as the energy of the particle approaches infinity fora fixed box length, L. Hint: it is more intuitive to do this graphically though it is easy to doanalytically.

Reference no: EM13633551

Questions Cloud

If this is the only possible means of cooling how many : a 5000 african elephant has a resting metabolic rate of 2500 . on a hot day the elephants environment is likely to be

A flask of water is connected to a vacuum pump a fewmoments : 1.the relative humidity of air is equal to the ratio of thepartial pressure of water in the air to the equilibrium

The gear is to transmit 90 hp at 300 rpm what does the : aan 8-inch pitch diameter steel gear 3 inches thick face width is pressed onto a 2 inch diameter steel shafte30000000

When rubidium metal is exposed to air one rb atom is : when rubidium metal is exposed to air one rb atom is combined with two oxygen atoms. if 1.75g of rb is exposed to air

Show that the quantum mechanical probability : 1. the following questions regard the quantum mechanical particlein a box.a explain why the n0 solution is not allowed

A projectile is launched from a cannon it has an initial : a projectile is launched from a cannon it has an initial speed of 58 ms at an angle of 37 degrees above horizontal. the

Find power required by the compressor isothermal efficency : refrigerant r-134a flows through a refigeration system at a rate of 0.12 kgs . at the entrance to the adiabatic

A copper block is removed from a 306 oven and dropped into : a copper block is removed from a 306 oven and dropped into 1.30 of water at 20.5. the water quickly reaches 25.9 and

120 gr of steam at 102 degree celsius is pumped into a : 120 gr of steam at 102 degree celsius is pumped into a well insulated container holding 500 gr of h2o water at 35.0

User Account

All Pages