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Chapter 5: Q94CE (page 193)

Sketch蠄(x) . Would you expect this wave function to be the ground state? Why or why not?

Short Answer

Expert verified

The wave function cannot be in the ground state as it has two types of anti-nodes.

Step by step solution

01

Significance of a wave function 

The wave function is described as the properties of a particular wave that mainly satisfies the wave property. However, it also describes a particle鈥檚 wave characteristics.

02

Sketching the function

The wave function has been sketched below:

Here, in this diagram, it has been observed that at the midpoint, the wave function is zero. Apart from that, at the first and the final segment of the distance, the wave function is at its peak.

03

Determination of the state of the wave function

According to the sketch of the wave function, the wave function cannot be in the ground state as it has two types of anti-nodes. Hence, the function should be at the first excited state.

Thus,

The wave function cannot be in the ground state as it has two types of anti-nodes.

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Most popular questions from this chapter

The particle has E=0.

(a) Show that the potential energy for x>0is given by

U(x)=-鈩�2am1x+鈩�2a22m

(b) What is the potential energy for x<0?

To determine the energy quantization condition

For a total energy of 0, the potential energy is given in Exercise 96. (a) Given these, to what region of the x-axis would a classical particle be restricted? Is the quantum-mechanical particle similarly restricted? (b) Write an expression for the probability that the (quantum-mechanical) particle would be found in the classically forbidden region, leaving it in the form of an integral. (The integral cannot be evaluated in closed form.)

The quantized energy levels in the infinite well get further apart as n increases, but in the harmonic oscillator they are equally spaced.

  1. Explain the difference by considering the distance 鈥渂etween the walls鈥� in each case and how it depends on the particles energy
  2. A very important bound system, the hydrogen atom, has energy levels that actually get closer together as n increases. How do you think the separation between the potential energy 鈥渨alls鈥� in this system varies relative to the other two? Explain.

Prove that the transitional-state wave function (5.33) does not have a well-defined energy.
See all solutions

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