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3. Show that the probability associated with tha state dimensional box 0≤x≤L Yn Pr(0 ≤ x ≤ 4) = Pr( ³1 ≤ x ≤ L) 4 for a particle in a one- obeys the following relationship:

3. Show that the probability associated with tha state dimensional box 0≤x≤L Yn Pr(0 ≤ x ≤ 4) = Pr( ³1 ≤ x ≤ L) 4 for a particle in a one- obeys the following relationship:

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Show that the probability associated with the state Ψn for a particle in a one- dimensional box 0≤ x≤ L obeys the following relationship: (You can see the picture attached for the problem)

 

 

**Problem Statement: Quantum Mechanics** 3. Show that the probability associated with the state \( \psi^n \) for a particle in a one-dimensional box \( 0 \leq x \leq L \) obeys the following relationship: \[ \Pr(0 \leq x \leq \frac{L}{4}) = \Pr(\frac{3L}{4} \leq x \leq L) \] (Note: This problem involves verifying the symmetry of the probability distribution for a particle in a quantized box over specified intervals. This showcases quantum mechanical principles such as wave function symmetry and probability conservation.)
Transcribed Image Text:**Problem Statement: Quantum Mechanics** 3. Show that the probability associated with the state \( \psi^n \) for a particle in a one-dimensional box \( 0 \leq x \leq L \) obeys the following relationship: \[ \Pr(0 \leq x \leq \frac{L}{4}) = \Pr(\frac{3L}{4} \leq x \leq L) \] (Note: This problem involves verifying the symmetry of the probability distribution for a particle in a quantized box over specified intervals. This showcases quantum mechanical principles such as wave function symmetry and probability conservation.)
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