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In this problem the probability density for the position of a particle with wave function ¥(x, 1) is denoted by p(x, 1). In general, the value of p(x, t) in a particular region will change with time and this change can be attributed to the flow of probability into and out of the region. Indeed we expect that there is a probability current density j(x, 1) which obeys the continuity equation ap aj at ax When there are many particles, the actual current of particles is obtained by multiplying j(x, 1) by the actual density of particles. (a) By noting that the time dependence of the wave function is governed by the Schrödinger equation, ih 2m ax²

In this problem the probability density for the position of a particle with wave function ¥(x, 1) is denoted by p(x, 1). In general, the value of p(x, t) in a particular region will change with time and this change can be attributed to the flow of probability into and out of the region. Indeed we expect that there is a probability current density j(x, 1) which obeys the continuity equation ap aj at ax When there are many particles, the actual current of particles is obtained by multiplying j(x, 1) by the actual density of particles. (a) By noting that the time dependence of the wave function is governed by the Schrödinger equation, ih 2m ax²

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In this problem the probability density for the position of a particle with wave function ¥(x, 1) is denoted by p(x, 1). In general, the value of p(x, t) in a particular region will change with time and this change can be attributed to the flow of probability into and out of the region. Indeed we expect that there is a probability current density j(x, 1) which obeys the continuity equation ap aj at ax When there are many particles, the actual current of particles is obtained by multiplying j(x, 1) by the actual density of particles. (a) By noting that the time dependence of the wave function is governed by the Schrödinger equation, ih 2m ax²
Transcribed Image Text:In this problem the probability density for the position of a particle with wave function ¥(x, 1) is denoted by p(x, 1). In general, the value of p(x, t) in a particular region will change with time and this change can be attributed to the flow of probability into and out of the region. Indeed we expect that there is a probability current density j(x, 1) which obeys the continuity equation ap aj at ax When there are many particles, the actual current of particles is obtained by multiplying j(x, 1) by the actual density of particles. (a) By noting that the time dependence of the wave function is governed by the Schrödinger equation, ih 2m ax²
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