We have investigated Nanostructure Physics of a Quantum Well (QW) adjacent to a tunnel barrier. On the other side of the QW, we have a barrier layer of semi-infinite thickness. The book contains thorough and complete analytical calculations leading to two transcendental equations obeyed by quasi-bound energy levels of the QW. The book also contains numerical investigation of parametric variations of the quasi-bound energy levels. The variations are quite unexpected. For some values of tunnel barrier width and height, each quasi-bound energy level yields two allowed energy levels. The two equations reduce to those for isolated QW in proper limiting values of parameters. The book contains necessary background on Quantum Mechanics, Microelectronics and Nanostructure Physics to enable readers assimilate the book completely.

*isolated*quantum well (QW)

**1.1 Wave equation of a free particle: Schrödinger equation**

**1.2 Schrödinger equation of a particle subject to a conservative mechanical**

**force**

**1)**A comparison of

*operator*

*operator*

*formalism*in quantum mechanics. Thus the operator of x is x, operator of p is

**2)**The Schrödinger equation of a free particle is

**3)**If a conservative force acts on a particle, the total energy E =

**4)**Using the operator correspondences of E, p and V,

*Hamiltonian*operator.

**1.3 Allowed values of an observable**

**1.4 Eigenvalue equation, eigenfunction and eigenvalue**

*eigenvalue equation*, where is called

*eigenfunction*and

*a*is called

*eigenvalue*. A is operator of the observable.

**1.5 Time-independent Schrödinger equation and stationary state.**

**1.6 Continuous and discontinuous function**

**1.7 Finite and infinite discontinuity**

**1.8 Admissibility conditions on wave function**

**1.**

**2.**

**3.**

**4.**

**5.**

**1.9 Calculation of confined energy levels of**

*isolated*quantum well (QW)

**(1.23)**

**(1.24)**

**(1.25)**

**(1.26)**

**2.1 Insulator and its band model**

**Figure 2.1:**Band model of insulator (at 0 K). The energy gap E