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2. Suppose a particle of mass, m, has energy E, and wave function: WE(x,t = 0) = Aeik + Be-ik What is WE(x, t)? Calculate the probability density of the particle when it has the wavefunction, e (x, t). If you wish to simply your answer algebraically, use this information: let A = aeia and B = beiß and A a-B, where the variables a, b, a, ß are all real! WARNING: Simplifying the equation is somewhat time consuming. Show/explain why y(x,t) is not normalizable. According to quantum theory, all physical systems must have an associated wavefunction that is normalizable. Explain why plane wave solutions to Schrodinger's equation are used in quantum theory, despite not being normalizable?

2. Suppose a particle of mass, m, has energy E, and wave function: WE(x,t = 0) = Aeik + Be-ik What is WE(x, t)? Calculate the probability density of the particle when it has the wavefunction, e (x, t). If you wish to simply your answer algebraically, use this information: let A = aeia and B = beiß and A a-B, where the variables a, b, a, ß are all real! WARNING: Simplifying the equation is somewhat time consuming. Show/explain why y(x,t) is not normalizable. According to quantum theory, all physical systems must have an associated wavefunction that is normalizable. Explain why plane wave solutions to Schrodinger's equation are used in quantum theory, despite not being normalizable?

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**2. Quantum Particle Wavefunction Analysis** Suppose a particle of mass, \( m \), has energy \( E \), and wave function: \[ \psi_E(x, t = 0) = Ae^{ikx} + Be^{-ikx}. \] **What is \( \psi_E(x, t) \)?** **Task:** Calculate the probability density of the particle when it has the wavefunction, \( \psi_E(x, t) \). If you wish to simplify your answer algebraically, use this information: let \( A = ae^{i\alpha} \) and \( B = be^{i\beta} \) and \(\Delta = \alpha - \beta\), where the variables \( a, b, \alpha, \beta \) are all real. **WARNING:** Simplifying the equation is somewhat time consuming. **Show/explain why \( \psi(x, t) \) is not normalizable.** According to quantum theory, all physical systems must have an associated wavefunction that is normalizable. Explain why plane wave solutions to Schrödinger's equation are used in quantum theory, despite not being normalizable.
Transcribed Image Text:**2. Quantum Particle Wavefunction Analysis** Suppose a particle of mass, \( m \), has energy \( E \), and wave function: \[ \psi_E(x, t = 0) = Ae^{ikx} + Be^{-ikx}. \] **What is \( \psi_E(x, t) \)?** **Task:** Calculate the probability density of the particle when it has the wavefunction, \( \psi_E(x, t) \). If you wish to simplify your answer algebraically, use this information: let \( A = ae^{i\alpha} \) and \( B = be^{i\beta} \) and \(\Delta = \alpha - \beta\), where the variables \( a, b, \alpha, \beta \) are all real. **WARNING:** Simplifying the equation is somewhat time consuming. **Show/explain why \( \psi(x, t) \) is not normalizable.** According to quantum theory, all physical systems must have an associated wavefunction that is normalizable. Explain why plane wave solutions to Schrödinger's equation are used in quantum theory, despite not being normalizable.
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