What values of energy do you expect probability density peak

Reference no: EM13535741

You have carefully prepared the wave function of an electron to be in the first energy eigenstate of an infinite potential well spanning a length a. Now you decide to release the electron from the prison by turning off the infinite potential barrier. The electron thus becomes free to move with zero potential everywhere. Your aim now is to make an immediate measurement of the energy of the electron and verify that the probabilities work according to the laws of quantum mechanics.

a) To do this you first need to calculate the fourier component of the initial wave function. [Hint: It is useful to express the sinusoidal function as a linear combination of exponentials using Euler's formulas.]

b) Simplify your answer by rewriting the exponentials in terms of sines and cosines. What is the energy associated with a fourier component k? Now, you can find the probability density of finding the particle with energy E.

c) For very large and very small values of k (or E), what happens to this probability density?

d) Intuitively, at what values of energy do you expect the probability density to peak?

Reference no: EM13535741

Questions Cloud

A beam of light is incident on a plane mirror : A beam of light is incident on a plane mirror at an angle of 32 degrees relative to the normal. What is the angle between the reflected rays and the surface of the mirror?

What will be the temperature of the brakes : An automobile has a mass of 1500 kg, and its aluminum brakes have an overall mass of 6.00 kg. (a) Assume all the mechanical energy that transforms into internal energy when the car stops is deposited in the brakes and no energy is transferred out of ..

Imagine a sphere of radius r filled with negative charge : Imagine a sphere of radius R filled with negative charge of uniform charge density. The total charge is equivalent to the charge of two electrons. Now insert two protons into the sphere and assume that in spite of their presence, the negative charge ..

What is the relative magnitude of the third charge : Three positively charged particles are constrained to move on a fixed circular track. If all charges were equal, the particles would be spaced 120 degrees apart. Now suppose that two charges are equal and they are spaced 90 degrees apart in the equil..

What values of energy do you expect probability density peak : You have carefully prepared the wave function of an electron to be in the first energy eigenstate of an infinite potential well spanning a length a. Now you decide to release the electron from the prison by turning off the infinite potential barri..

Block of mass m is initially at rest on frictionless surface : A block of mass m is initially at rest on a frictionless surface. At time t = 0, an increasing force given by F = kt2 is applied to the block. Find the velocity and the displacement of the block as a function of time and graph x and v versus t.

Coefficient of friction between the box and the floor : A man pushes a box of mass M with a force F using a stick AB of mass m and making a angle θ with the vertical. The coefficient of friction between the box and the floor is μ. Draw a clear diagram showing all the forces.

Velocity v of waves on vibrating string depends on tension : The velocity v of waves on a vibrating string depends on the tension T in the string and the mass per unit length λ of the string. Derive an expression for v by using the dimensional analysis method

A spelunker drops a stone from rest into a hole : A spelunker (cave explorer) drops a stone from rest into a hole. The speed of sound is 343 m/s in air, and the sound of the stone striking the bottom is heard 4.88 s after the stone is dropped. How deep is the hole?

User Account

All Pages