Undergrad Probability of finding a particle in a 1-D box max. at centre?

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The probability density for a particle in a one-dimensional box is maximized at the center due to the wave function's characteristics in the ground state (n=1). This central peak indicates the highest likelihood of finding the particle at that position. In excited states with larger quantum numbers (n), the probability distribution becomes more uniform, reflecting the increased energy levels. The behavior of the probability density is directly related to the standing wave patterns formed within the box. Understanding these concepts is crucial for grasping quantum mechanics principles.
Apashanka
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Probability density ##(2/L)*sin^2(\pi x/L)##
From the probability density plot why it is max at the centre of the box...e.g probability to find the particle per unit le gth is max. at the centre of the box??why not at any other position??
 
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You say about the ground state n=1. As for excited states for larger n you will see almost homogeneous distribution as you may expect.
 

Thread 'Two equivalent statements of time reversal symmetric Hamiltonian'

Time reversal invariant Hamiltonians must satisfy ##[H,\Theta]=0## where ##\Theta## is time reversal operator. However, in some texts (for example see Many-body Quantum Theory in Condensed Matter Physics an introduction, HENRIK BRUUS and KARSTEN FLENSBERG, Corrected version: 14 January 2016, section 7.1.4) the time reversal invariant condition is introduced as ##H=H^*##. How these two conditions are identical?
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