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(a) Write down the wave function of this particle. (b) Express the total energy of this particle in terms of m (a and b have dimensionless unit)

(a) Write down the wave function of this particle. (b) Express the total energy of this particle in terms of m (a and b have dimensionless unit)

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answer part a and b

The normalized wave function of a particle (with mass \( m \)) in a two-dimensional box \((0 \leq x \leq a; 0 \leq y \leq b; a = 2, b = 4)\) is illustrated in the following two figures. **Figure Descriptions:** 1. **Left Figure (\(\psi(x)\)):** - This graph represents the wave function \(\psi(x)\) along the x-axis for a particle in a two-dimensional box. - The horizontal axis is labeled from 0 to 2, corresponding to the boundary \(a = 2\). - The vertical axis represents the wave function \(\psi(x)\). - The graph shows a sinusoidal wave pattern starting from zero, oscillating symmetrically about the horizontal axis. 2. **Right Figure (\(\psi(y)\)):** - This graph represents the wave function \(\psi(y)\) along the y-axis. - The horizontal axis is labeled from 0 to 4, corresponding to the boundary \(b = 4\). - The vertical axis represents the wave function \(\psi(y)\). - The graph illustrates a sinusoidal wave, similar to \(\psi(x)\), but with more oscillations due to the larger boundary along the y-axis. These graphs visualize the behavior of the wave functions within the defined boundaries of the two-dimensional box.
Transcribed Image Text:The normalized wave function of a particle (with mass \( m \)) in a two-dimensional box \((0 \leq x \leq a; 0 \leq y \leq b; a = 2, b = 4)\) is illustrated in the following two figures. **Figure Descriptions:** 1. **Left Figure (\(\psi(x)\)):** - This graph represents the wave function \(\psi(x)\) along the x-axis for a particle in a two-dimensional box. - The horizontal axis is labeled from 0 to 2, corresponding to the boundary \(a = 2\). - The vertical axis represents the wave function \(\psi(x)\). - The graph shows a sinusoidal wave pattern starting from zero, oscillating symmetrically about the horizontal axis. 2. **Right Figure (\(\psi(y)\)):** - This graph represents the wave function \(\psi(y)\) along the y-axis. - The horizontal axis is labeled from 0 to 4, corresponding to the boundary \(b = 4\). - The vertical axis represents the wave function \(\psi(y)\). - The graph illustrates a sinusoidal wave, similar to \(\psi(x)\), but with more oscillations due to the larger boundary along the y-axis. These graphs visualize the behavior of the wave functions within the defined boundaries of the two-dimensional box.
### Quantum Mechanics Problem **(a)** Write down the wave function of this particle. **(b)** Express the total energy of this particle in terms of \( m \) \((a \text{ and } b \text{ have dimensionless unit})\). --- This problem requires understanding of quantum mechanics, particularly in expressing wave functions and calculating total energy. The variables \( a \) and \( b \) are dimensionless. The context of this problem typically involves solving Schrödinger's equation for a given system to determine the wave function and then using that information to find the energy levels.
Transcribed Image Text:### Quantum Mechanics Problem **(a)** Write down the wave function of this particle. **(b)** Express the total energy of this particle in terms of \( m \) \((a \text{ and } b \text{ have dimensionless unit})\). --- This problem requires understanding of quantum mechanics, particularly in expressing wave functions and calculating total energy. The variables \( a \) and \( b \) are dimensionless. The context of this problem typically involves solving Schrödinger's equation for a given system to determine the wave function and then using that information to find the energy levels.
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a=2 and b=4

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