Question

Sketch the wave-function of the ground state of a particle of mass m which is con- fined in one dimension within a square potential well of infinite height, centred at x = 0 and of width a between x = ?a/2 and x = a/2.

What type of function is that?

If the infinite potential well is replaced by a potential well of finite height, sketch the new ground state wave-function. Explain qualitatively how the ground state energy changes in going to the finite well.

Answer 1

la función de onda del estado base de una partícula de masa m que está confinada en una dimensión dentro de un pozo potencial cuadrado de altura infinita, centrada en x = 0 y de ancho a entre x =? a / 2 y x = a / 2.

the base state or ground state corresponds to n = 1.

la función es de tipo sinusoidal

If the total energy E of the system is less than U, according to classical physics the particle would be permanently bound in the potential well. If the particle were outside the well, its kinetic energy would have to be nagative, which would be impossible. According to quantum mechanics there is a finite possibility that the particle may be outside the well. (region I for x minor to -a / 2 and region III for x greater than a / 2). This may seem strange, but the uncertainty principle tells us that the energy of the system is uncertain. This allows the particle to be out of the well while the apparent violation of the energy conservation does not exist in any way possible to measure.