R-ckay said:[itex]\int[/itex](boundary a to 0) |ψ(x,0)|^2=[ √6/√5sin(∏x/a)+2/√5sin(2∏x/a)][√6/√5sin(∏x/a)+2/√5sin(2∏x/a]
[itex]\int[/itex] [6/5(sin(∏x/a))^2+2√6/5sin(∏x/a)sin(∏x/a)+2√6/5sin(∏x/a)sin(2∏x/a)+4/5(sin(2∏x/a))^2
but I didn't find the final value. there's still "a" in the final result instead of a number of probability.
The presence of ##a## is not really a problem. What exactly are you trying to do here?R-ckay said:[itex]\int[/itex](boundary a to 0) |ψ(x,0)|^2=[ √6/√5sin(∏x/a)+2/√5sin(2∏x/a)][√6/√5sin(∏x/a)+2/√5sin(2∏x/a]
[itex]\int[/itex] [6/5(sin(∏x/a))^2+2√6/5sin(∏x/a)sin(∏x/a)+2√6/5sin(∏x/a)sin(2∏x/a)+4/5(sin(2∏x/a))^2
but I didn't find the final value. there's still "a" in the final result instead of a number of probability.
A particle in a box is a theoretical model used in quantum mechanics to describe a particle confined within a finite space. The particle is assumed to have no interaction with the walls of the box, and its energy is quantized due to the boundary conditions.
The probability of finding a particle in a particular location within the box is calculated using the Schrödinger equation, which takes into account the particle's wave function and the potential energy of the box. The square of the wave function represents the probability density, which is used to calculate the probability of finding the particle in a specific region.
The probability of finding a particle in a box is inversely proportional to the size of the box. As the box becomes smaller, the energy levels become more closely spaced, leading to a higher probability of finding the particle in a specific region. Conversely, as the box becomes larger, the energy levels become more spread out, resulting in a lower probability of finding the particle in a specific region.
In theory, the probability of finding a particle in a box can never be 100%. This is because the uncertainty principle in quantum mechanics states that it is impossible to know both the exact position and momentum of a particle simultaneously. However, as the size of the box decreases, the probability of finding the particle within a certain range approaches 100%.
The energy of a particle in a box is directly related to the size of the box. As the size of the box increases, the energy levels also increase. This is due to the fact that a larger box allows for more possible states for the particle to occupy, resulting in a greater range of energy levels. Conversely, a smaller box restricts the possible states and thus leads to lower energy levels.