Thejas15101998 said:I think the reason is that during derivation we get ka=n (wavelength ) and thus n being negative implies that wavelength is negative hence contradiction.
How does the wave function change for e.g. the second eigenstate if you replace n = +2 with n = -2? Does this make any difference in physically measurable quantities?Thejas15101998 said:In the 1D particle in a box system why don't we take negative integer values of n besides the positive integer values?
A particle in a 1D box system is a simplified model used in quantum mechanics to study the behavior and properties of a particle confined in a one-dimensional space. The particle is assumed to have zero potential energy outside of the box and infinite potential energy within the box, creating a well-defined and bounded system.
The energy of a particle in a 1D box can be calculated using the Schrödinger equation, which is a fundamental equation in quantum mechanics. The energy levels are quantized, meaning they can only take on certain discrete values determined by the size of the box and the mass of the particle.
The size of the box directly affects the energy levels of the particle in a 1D box system. As the size of the box decreases, the energy levels become more closely spaced, and the energy of the particle increases. Conversely, as the size of the box increases, the energy levels become more widely spaced, and the energy of the particle decreases.
The particle in a 1D box system is a simple yet important model in quantum mechanics. It allows us to understand the behavior of a particle in a confined space and provides a foundation for more complex systems. It also demonstrates the concept of quantization in energy levels, which is a fundamental principle in quantum mechanics.
While the particle in a 1D box system is a simplified model and cannot fully represent real-world systems, it can be applied to certain scenarios. For example, it can be used to study the behavior of electrons in a nanoscale semiconductor device or the vibrations of atoms in a solid material. However, it should be noted that the model has limitations and cannot fully capture all aspects of these real-world systems.