- #31
Finding the expected value of position in a Potential Well
- Thread starter ja07019
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Homework Help Overview
The discussion revolves around a problem involving an electron trapped in a potential well, specifically focusing on the wave function derived from the Schrödinger Equation. The original poster expresses difficulty in determining the appropriate wave function, noting that their calculations yield results differing from the textbook. The problem involves calculating the expected value of a specific expression related to the position of the electron within the well.
Discussion Character
- Exploratory, Conceptual clarification, Mathematical reasoning, Problem interpretation, Assumption checking
Approaches and Questions Raised
- Participants discuss the nature of the wave function, with some emphasizing the importance of boundary conditions and the separation of variables. There are attempts to compute integrals related to the expected value, and questions arise regarding the validity of using complex exponentials in the context of the problem. The distinction between symmetric and asymmetric solutions is also explored.
Discussion Status
There is ongoing exploration of the wave function solutions and their implications for the expected value calculations. Some participants have provided guidance regarding the need for boundary conditions and the role of integration constants, while others are questioning the assumptions made about the wave functions and their forms.
Contextual Notes
Participants note that the potential well is one-dimensional, extending from -L to L, and there is a discussion about the implications of using complex exponentials in the wave function. The original poster has indicated confusion regarding the expected value calculations and the relationship between the symmetric and asymmetric solutions.
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