Bootstrapping in Quantum Mechanics uses positivity condition to derive the eigenspectum. For non-hermitian systems usual does not work. In this paper we define for special class of Hamiltonian, PT symmetric Hamiltonian. We illustrate modified with several examples and obtain eigenspectrum.

We incorporate the microscopic assumptions that lead to a certain generalization of Lieb-Schultz-Mattis (LSM) theorem for one-dimensional spin chains into conformal bootstrap. Our approach accounts ``LSM anomaly'' possessed by these through combination modular bootstrap and correlator symmetry defect operators. Specifically, we obtain universal bounds on local operator content $(1+1)d$ field th...

Recently, bootstrap methods from conformal field theory have been adapted for studying the energy spectrum of various quantum mechanical systems. In this paper, we consider application these in obtaining Schr\"odinger equation with periodic potentials, paying particular attention to Kronig-Penney model a particle one-dimensional lattice. With an appropriate choice operator basis involving posit...

Gravitational interferometers and cosmological observations of the cosmic microwave background offer us prospect to probe laws gravity in primordial universe. To study interpret these datasets we need know possible graviton non-Gaussianities. this end, derive most general tree-level three-point functions (bispectra) for a massless all orders derivatives, assuming scale invariance. Instead worki...