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1. Consider a one-dimensional rectangular potential barrier V(x): V(2) – {v. So z(0, z)a 0(z(a (1) where Vo is positive. A particle with energy E < V, approaches the barrier from the left (see figure Fig. 1). E 3 x=a Figure 1 i Find in each region the wave function by solving the Schrodinger equation. ii By definition, the transmission coefficient T is defined as the transmitted current divided by the incident current: Jranamatted T Jmesdent where j 2mi evaluate T in terms of the amplitudes of transmitted and incident wave functions. iii Using the boundary conditions prove that: T = where ka 1+ sinh kya is the wave vector in region 2.

1. Consider a one-dimensional rectangular potential barrier V(x): V(2) – {v. So z(0, z)a 0(z(a (1) where Vo is positive. A particle with energy E < V, approaches the barrier from the left (see figure Fig. 1). E 3 x=a Figure 1 i Find in each region the wave function by solving the Schrodinger equation. ii By definition, the transmission coefficient T is defined as the transmitted current divided by the incident current: Jranamatted T Jmesdent where j 2mi evaluate T in terms of the amplitudes of transmitted and incident wave functions. iii Using the boundary conditions prove that: T = where ka 1+ sinh kya is the wave vector in region 2.

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1. Consider a one-dimensional rectangular potential barrier V(x): z(0, r)a 0(r(a V(x) - (1) where Vo is positive. A particle with energy E < V, approaches the barrier from the left (see figure Fig. 1). 2 E 1 3 x=0 x=a Figure 1 i Find in each region the wave function by solving the Schrodinger equation. ii By definition, the transmission coefficient T is defined as the transmitted current divided by the incident current: T- İranamtted Jimetdent where j 2mi (2) evaluate T in terms of the amplitudes of transmitted and incident wave functions. iii Using the boundary conditions prove that: T = where k2 1+E Ninh? kga is the wave vector in region 2.
Transcribed Image Text:1. Consider a one-dimensional rectangular potential barrier V(x): z(0, r)a 0(r(a V(x) - (1) where Vo is positive. A particle with energy E < V, approaches the barrier from the left (see figure Fig. 1). 2 E 1 3 x=0 x=a Figure 1 i Find in each region the wave function by solving the Schrodinger equation. ii By definition, the transmission coefficient T is defined as the transmitted current divided by the incident current: T- İranamtted Jimetdent where j 2mi (2) evaluate T in terms of the amplitudes of transmitted and incident wave functions. iii Using the boundary conditions prove that: T = where k2 1+E Ninh? kga is the wave vector in region 2.
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