The discussion centers on the harmonic oscillator in quantum mechanics, specifically analyzing the potential energy function V(x) = ½Kx² and the state function u(¥) = B¥exp(+¥²/2). Participants debate whether this state function qualifies as an energy eigenstate of the system. Additionally, they explore the probability per unit length of measuring the particle at position x=0 at a time t=t0>0, emphasizing the necessity of prior effort in problem-solving before seeking assistance.
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As you well know, the forum rules prohibit us from providing you with help unless you have shown some effort in solving the problem yourself.physics2004 said:A particle of mass m moves along the x-direction such that V(x)=½Kx^2. Is the state u(¥)=B¥exp(+¥2/2), where ¥ is Hx (H = constant), an energy eigenstate of the system?. What is probability per unit length for measuring the particle at position x=0 at t=t0>0?