Consider a quantum particle described by the wave function: (See pisture above) where E1 is the eigenvalue of 𝜓1 and E2 is the eigenvalue of 𝜓2. The functions 𝜓1 and 𝜓2 are part of a complete set of functions of the one-dimensional particle-in-the-box model and

The wave function of any system can be written as the linear combination of all possible state of th...

Resuelto Consider a quantum particle described by the wave

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Pregunta: Consider a quantum particle described by the wave function: (See pisture above) where E1 is the eigenvalue of 𝜓1 and E2 is the eigenvalue of 𝜓2. The functions 𝜓1 and 𝜓2 are part of a complete set of functions of the one-dimensional particle-in-the-box model and
Consider a quantum particle described by the wave function: (See pisture above) where E1 is the eigenvalue of 𝜓1 and E2 is the eigenvalue of 𝜓2. The functions 𝜓1 and 𝜓2 are part of a complete set of functions of the one-dimensional particle-in-the-box model and correspond to the ground state and the first excited level, respectively.
(a.)Show that 𝜓12 is normalized.
(b.) What is the average value of the energy for this system, 〈𝐸〉?
Muestra el texto de la transcripción de la imagen
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Texto de la transcripción de la imagen:

ψ_{12} = \frac{1}{3} ψ_{1} + \frac{2}{3} ψ_{2}

donde

E_{1}

es el valor propio de

ψ_{1}

E_{2}

es el valor propio de

ψ_{2}

. Las funciones

ψ_{1}

ψ_{2}

forman parte de un conjunto completo de funciones propias del modelo de la partícula en la caja en una dimensión y corresponden al estado raso y el primer nivel excitado, respectivamente. a. (10) Demuestre que

ψ_{12}

está normalizada. b. (10) ¿Cuál es el valor promedio de la energía para este sistema,

⟨ E ⟩

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Pregunta: Consider a quantum particle described by the wave function: (See pisture above) where E1 is the eigenvalue of 𝜓1 and E2 is the eigenvalue of 𝜓2. The functions 𝜓1 and 𝜓2 are part of a complete set of functions of the one-dimensional particle-in-the-box model and

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