Exam 18: Introduction to Quantum Mechanics

The graph below represents a wave function $\Psi$ (x) for a particle confined to -2.00 m $\le$ x $\le$ +2.00 m.The value of the normalisation constant A may be:

A particle has a total energy that is less than that of a potential barrier.When the particle penetrates the barrier, its wave function is:

When U(x) is infinitely large elsewhere, the wave function of a particle restricted to the region 0 < x < L where U(x) = 0, may have the form $\Psi$ (x) =

A physically reasonable wave function, $\Psi$ (x), for a one-dimensional system must:

What is the quantum number n of a particle of mass m confined to a one-dimensional box of length L when its momentum is 4h/L?

The wave function $\Psi$ (x) of a particle confined to 0 $\le$ x $\le$ L is given by $\Psi$ (x) = Ax. $\Psi$ (x) = 0 for x < 0 and x > L.When the wave function is normalised, the probability density at coordinate x has the value:

The expectations value of a function f(x) of x when the wave function depends only on x is given by < f(x) > =

Assume we can determine the position of a particle within an uncertainty of 0.5 nm.What will be the resulting uncertainty in the particle's momentum (in kg . m/s)?

Find the uncertainty in the momentum (in kg .m/s) of an electron if the uncertainty in its position is equal to 3.4 * 10-10 m, the circumference of the first Bohr orbit.

Find the kinetic energy (in terms of Planck's constant) of a football (m = 1 kg) confined to a one-dimensional box that is 25 cm wide if the baseball can be treated as a wave in the ground state.

The wave function for a particle in a one-dimensional box is .Which statement is correct?

If the position of an electron (m = 9.11 *10-31 kg) could be measured to within 10^-30 m, the uncertainty in the magnitude of its speed could be as much as

A particle in a finite potential well has energy E, as shown below. The wave function in region III where x > L has the form $\Psi$ III =

A particle is in the second excited state of a one-dimensional box of length 1.0 m.What is its momentum (in kg . m/s)?

An electron is sitting on a pinpoint having a diameter of 2.5 $\mu$ m.What is the minimum uncertainty in the speed of the electron?

The graph below shows the value of the probability density $\Psi$ (x)|2 in the region-3.00 m $\le$ x $\le$ +3.00 m.The value of the constant A is:

If the interaction of a particle with its environment restricts the particle to a finite region of space, the result is the quantisation of ____ of the particle.

Because the factor h on the right side of the Heisenberg uncertainty principle has units of Joule-seconds, it suggests that the energy of a system also has uncertainty.The uncertainty in energy depends on the length of the time interval during which a system exists. $\Delta$ E $\Delta$ t $\ge$ h/4 $\pi$ .Suppose an unstable mass is produced during a high-energy collision such that the uncertainty in its mass is me/100.(me = 9.11*10-31 kg.) How long will this particle exist?

A particle is in the ground state of a one-dimensional box of length 1.0 m.What is the minimum value of its momentum (in kg .m/s)?

Suppose we use optical radiation ( $\lambda$ = 500 nm) to determine the position of the electron to within the wavelength of the light.What will be the resulting uncertainty in the electron's velocity?