Understanding the Quantum Mechanical Model for V = Infinity and V = kx2/2

In summary, the problem involves finding the energies and wave functions for a quantum mechanical model with a potential of infinity for x less than or equal to 0 and kx2/2 for x greater than or equal to 0. This can be solved by using the 1-D particle in a box and harmonic oscillator equations, and then joining the solutions at x=0.
  • #1
hamilton5
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Homework Statement


What are the energies and wave functions for the quantum mechanical model where V = infinity for x less than or equal to 0 and V = kx2/2 for x greater than or equal to 0?


Homework Equations


1-D particle in a box E = (h2/8m)(n2/L2)

Harmonic Oscillator E = (v + 1/2)(h/2*pi)w


The Attempt at a Solution


Honestly, I had no clue where to start. This was the last problem on our first exam. I tried drawing what it would represent graphically but I'm not really sure what I was supposed to answer... Do I add the energies together? Wave functions? I'm not even sure what format our professor was looking for he didn't tell us...
 
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  • #2
Solve the Schrodinger equation in each region, x<0 and x>0, and then join the solutions at x=0.
 

Related to Understanding the Quantum Mechanical Model for V = Infinity and V = kx2/2

1. What is Physical Chemistry 2 and why is it important?

Physical Chemistry 2 is a branch of chemistry that focuses on the study of the physical properties and behavior of matter at a molecular and atomic level. It is important because it helps us understand the fundamental principles of chemical reactions and the properties of materials, which has practical applications in various fields such as medicine, materials science, and energy production.

2. What are some common topics covered in Physical Chemistry 2?

Some common topics covered in Physical Chemistry 2 include thermodynamics, chemical kinetics, quantum mechanics, electrochemistry, and spectroscopy.

3. How is Physical Chemistry 2 different from other branches of chemistry?

Physical Chemistry 2 differs from other branches of chemistry in that it focuses on the study of the physical properties and behavior of matter at a molecular and atomic level, rather than the composition and synthesis of compounds.

4. What are some real-world applications of Physical Chemistry 2?

Physical Chemistry 2 has numerous real-world applications, such as designing new materials for use in electronics or medical devices, developing more efficient energy sources, and understanding and predicting the behavior of chemical reactions in industrial processes.

5. How can I improve my understanding of Physical Chemistry 2 problems?

To improve your understanding of Physical Chemistry 2 problems, it is important to have a strong foundation in fundamental concepts and principles. It also helps to practice solving different types of problems and to seek help from peers or instructors when needed.

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